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## Liu, Zhengrong

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 Author ID: liu.zhengrong Published as: Liu, Z.; Liu, Zheng Rong; Liu, Zheng-Rong; Liu, Zheng-rong; Liu, Zhengrong
 Documents Indexed: 173 Publications since 1982, including 1 Book
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#### Co-Authors

 4 single-authored 16 Yu, Yuan-hong 15 Li, Jibin 10 Song, Ming 10 Tang, Hao 7 Huang, Zhehao 7 Zhu, Neng 6 Fu, Yanggeng 6 Jing, Zhujun 6 Pan, Chaohong 6 Shi, Shijie 6 Zhang, Bengong 5 Jin, Hai-Yang 5 Lin, Chang 5 Zhao, Kun 3 Biswas, Anjan 3 Chen, Yiren 3 Guo, Boling 3 Li, Shaoyong 3 Qian, Tifei 3 Wang, Zhenzhen 3 Wu, Yun 3 Xu, Jiao 3 Yang, Jiaopeng 2 Cao, Hongjun 2 Chen, Can 2 He, Xuezhong 2 Jiang, Tao 2 Li, Qixiu 2 Lin, Qingmei 2 Long, Yao 2 Luo, Jiaowan 2 Mao, Jianfeng 2 Ouyang, Zhengyong 2 Sun, Guozhang 2 Tian, Yanling 2 Wang, Fang 2 Wang, Ruiqi 2 Wen, Zhenshu 2 Xu, Juntao 2 Xu, Zhenyuan 2 Yang, Chenxi 2 Yang, Zhiyan 2 Zerrad, Essaid 2 Zhao, Xiaohua 2 Zhou, Yong 1 Cai, Huixian 1 Cao, Jinde 1 Chang, Yifang 1 Chen, Wendeng 1 Cheng, Dixiang 1 Fan, Jiashen 1 Feng, Zhaosheng 1 Ge, Weigao 1 Gerard, Raymond 1 He, Fusheng 1 Hu, Bambi 1 Huang, Xin 1 Jiang, Tianpei 1 Kayed, Ali Mohammed 1 Li, Chengyue 1 Li, Shao-Yong 1 Li, Zongguang 1 Liang, Yong 1 Lin, Shizhong 1 Liu, Bin 1 Liu, Erning 1 Luo, Shiyu 1 Martinez, Vincent R. 1 Pan, Jian 1 Shao, Mingzhu 1 Shen, Jiaqi 1 Tang, Jianning 1 Tian, Lixin 1 Wang, Kuanfu 1 Wei, Sirong 1 Wu, Chufen 1 Wu, Xiaoming 1 Xiao, Qing 1 Yan, Weifang 1 Yan, Yuexin 1 Yang, Lijun 1 Yang, Xingyu 1 Yang, Xiyan 1 Yao, Weiguo 1 Yi, Yating 1 Zhang, Shiqing 1 Zhang, Xiang 1 Zhao, Yongye 1 Zheng, Shan 1 Zhou, Shigang 1 Zhou, Zhengxin 1 Zhu, Xuena 1 Zhu, Zhaoxuan 1 Zhu, Zheng
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#### Serials

 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Applied Mathematics and Mechanics. (English Edition) 7 Chaos, Solitons and Fractals 7 Applied Mathematics and Computation 6 Journal of Mathematical Analysis and Applications 6 Acta Mathematicae Applicatae Sinica 6 Nonlinear Dynamics 5 Applied Mathematics Letters 5 Journal of Applied Mathematics 4 Mathematical Methods in the Applied Sciences 4 Journal of Differential Equations 3 Physics Letters. A 3 Kyungpook Mathematical Journal 3 Acta Mathematicae Applicatae Sinica. English Series 3 Annals of Differential Equations 3 Abstract and Applied Analysis 3 Nonlinear Analysis. Real World Applications 2 Journal of Kunming Institute of Technology 2 Science in China. Series A 2 Applied Mathematical Modelling 2 Kexue Tongbao 2 Chinese Science Bulletin 2 NoDEA. Nonlinear Differential Equations and Applications 2 Discrete and Continuous Dynamical Systems 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Journal of Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Acta Mathematica Sinica 1 Demonstratio Mathematica 1 Monatshefte für Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Soochow Journal of Mathematics 1 Journal of Mathematics. Wuhan University 1 Chinese Annals of Mathematics. Series B 1 Journal of East China Normal University. Natural Science Edition 1 Physica D 1 Journal of Systems Science and Mathematical Sciences 1 Acta Scientiarum Naturalium Universitatis Pekinensis 1 Acta Physica Sinica 1 Mathematica Applicata 1 Systems Science and Mathematical Sciences 1 Mathematics Journal of Toyama University 1 Bulletin of the Institute of Mathematics. Academia Sinica 1 SIAM Journal on Mathematical Analysis 1 Acta Mathematica Sinica. New Series 1 Journal of Partial Differential Equations 1 Journal of Dynamics and Differential Equations 1 Mathematical Problems in Engineering 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Journal of Inequalities and Applications 1 Acta Mathematica Sinica. English Series 1 Qualitative Theory of Dynamical Systems 1 Nonlinear Analysis. Modelling and Control 1 Journal of Zhejiang University. Engineering Science 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Journal of Yunnan University. Natural Sciences Edition 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 Communications in Mathematical Sciences 1 Journal of Yunnan Nationalities University. Natural Sciences Edition 1 Frontiers of Mathematics in China 1 Applied Mathematics & Information Sciences 1 Applicable Analysis and Discrete Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Advances in Mathematical Physics 1 Journal of Function Spaces 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 100 Partial differential equations (35-XX) 55 Ordinary differential equations (34-XX) 46 Dynamical systems and ergodic theory (37-XX) 15 Biology and other natural sciences (92-XX) 10 Fluid mechanics (76-XX) 9 Mechanics of deformable solids (74-XX) 7 Mechanics of particles and systems (70-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Probability theory and stochastic processes (60-XX) 3 Difference and functional equations (39-XX) 3 Numerical analysis (65-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH

110 Publications have been cited 1,082 times in 634 Documents Cited by Year
Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. Zbl 0985.37072
Li, Jibin; Liu, Zhengrong
2000
Traveling wave solutions for a class of nonlinear dispersive equations. Zbl 1011.35014
Li, Jibin; Liu, Zhengrong
2002
Peakons of the Camassa-Holm equation. Zbl 1018.35061
Liu, Zhengrong; Qian, Tifei
2002
A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations. Zbl 1203.35234
Liu, Zhengrong; Ouyang, Zhengyong
2007
Peakons and their bifurcation in a generalized Camassa-Holm equation. Zbl 1090.37554
Liu, Zhengrong; Qian, Tifei
2001
Peaked wave solutions of Camassa-Holm equation. Zbl 1068.35136
Liu, Zhengrong; Wang, Ruiqi; Jing, Zhujun
2004
The application of bifurcation method to a higher-order KdV equation. Zbl 1012.35076
Liu, Zhengrong; Yang, Chenxi
2002
Hamiltonian symmetric groups and multiple periodic solutions to delay differential equations. Zbl 0920.34061
Li, Jibin; He, Xue-Zhong; Liu, Zhengrong
1999
Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms. Zbl 0974.34038
Cao, Hongjun; Liu, Zhengrong; Jing, Zhujun
2000
New exact solutions for the classical Drinfel’d-Sokolov-Wilson equation. Zbl 1181.35221
Wen, Zhenshu; Liu, Zhengrong; Song, Ming
2009
Periodic cusp wave solutions and single-solitons for the $$b$$-equation. Zbl 1068.35103
Guo, Boling; Liu, Zhengrong
2005
Large-scale modes of turbulent channel flow: transport and structure. Zbl 1102.76314
Liu, Z.; Adrian, R. J.; Hanratty, T. J.
2001
Compacton-like wave and kink-like wave of GCH equation. Zbl 1106.35065
Liu, Zhengrong; Long, Yao
2007
Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations. Zbl 1220.34010
Zhang, Ben-Gong; Li, Shao-Yong; Liu, Zheng-Rong
2008
Peaked wave solutions of CH-r equation. Zbl 1089.35521
Guo, Boling; Liu, Zhengrong
2003
Two new types of bounded waves of CH-$$\gamma$$ equation. Zbl 1217.35161
Guo, Boling; Liu, Zhengrong
2005
The same distribution of limit cycles in five perturbed cubic Hamiltonian systems. Zbl 1074.34040
Liu, Zhengrong; Yang, Zhiyan; Jiang, Tao
2003
Bifurcation of peakons and periodic cusp waves for the generalization of the Camassa-Holm equation. Zbl 1218.35026
Wen, Zhenshu; Liu, Zhengrong
2011
New bounded traveling waves of Camassa-Holm equation. Zbl 1063.35138
Liu, Zhengrong; Li, Qixiu; Lin, Qingmei
2004
Periodic solutions to some differential delay equations created by Hamiltonian systems. Zbl 0946.34063
Li, Jibin; Liu, Zhengrong; He, Xuezhong
1999
New exact solitary wave and multiple soliton solutions of quantum Zakharov-Kuznetsov equation. Zbl 1200.35238
Zhang, Bengong; Liu, Zhengrong; Xiao, Qing
2010
Large time behavior of the full attraction-repulsion Keller-Segel system in the whole space. Zbl 1326.35042
Jin, Hai-Yang; Liu, Zhengrong
2015
The explicit nonlinear wave solutions and their bifurcations of the generalized Camassa-Holm equation. Zbl 1258.35050
Liu, Zhengrong; Liang, Yong
2011
Compactons in a general compressible hyperelastic rod. Zbl 1116.74374
Liu, Zhengrong; Chen, Can
2004
A note on the solution map for the periodic Camassa-Holm equation. Zbl 1310.35078
Tang, Hao; Zhao, Yongye; Liu, Zhengrong
2014
Bifurcations of solitary waves and domain wall waves for KdV-like equation with higher order nonlinearity. Zbl 1042.35067
Liu, Zhengrong; Li, Jibin
2002
Explicit periodic wave solutions and their bifurcations for generalized Camassa – Holm equation. Zbl 1202.35048
Liu, Zhengrong; Tang, Hao
2010
Coexistence of multifarious explicit nonlinear wave solutions for modified forms of Camassa-Holm and Degaperis-Procesi equations. Zbl 1176.34005
Liu, Zhengrong; Pan, Jian
2009
Well-posedness of the modified Camassa-Holm equation in Besov spaces. Zbl 1327.35345
Tang, Hao; Liu, Zhengrong
2015
Orbital stability of peakons with nonvanishing boundary for CH and CH-$$\gamma$$ equations. Zbl 1227.34018
Ouyang, Zheng-Yong; Zheng, Shan; Liu, Zheng-Rong
2008
Integral approach to compacton solutions of Boussinesq-like $$B$$($$m$$,$$n$$) equation with fully nonlinear dispersion. Zbl 1068.35135
Liu, Zhengrong; Lin, Qingmei; Li, Qixiu
2004
The dependences on initial data for the b-family equation in critical Besov space. Zbl 1319.35227
Tang, Hao; Shi, Shijie; Liu, Zhengrong
2015
On the connection between two parts of Hilbert’s 16th problem and equivariant bifurcation problem. Zbl 0967.34025
Li, Jibin; Liu, Zhengrong
1998
High order finite difference and multigrid methods for spatially evolving instability in a planar channel. Zbl 0769.76038
Liu, C.; Liu, Z.
1993
Continuous properties of the solution map for the Euler equations. Zbl 1293.35229
Tang, Hao; Liu, Zhengrong
2014
Non-uniform dependence on initial data for the periodic modified Camassa-Holm equation. Zbl 1268.35011
Fu, Yanggeng; Liu, Zhengrong
2013
Detection function method and its application to a perturbed quintic Hamiltonian system. Zbl 0994.37022
Liu, Zhengrong; Qian, Tifei; Li, Jibin
2002
Bifurcation set and distribution of limit cycles for a class of seven-order Hamiltonian system with fifteen-order perturbed terms. Zbl 0994.37024
Wang, Ruiqi; Liu, Zhengrong; Jing, Zhujun
2002
An analysis of the distortion and breakup mechanisms of high speed liquid drops. Zbl 1135.76481
Liu, Z.; Reitz, R. D.
1997
Boundedness and large time behavior of an attraction-repulsion chemotaxis model with logistic source. Zbl 1357.35050
Shi, Shijie; Liu, Zhengrong; Jin, Hai-Yang
2017
Singular soliton solution and bifurcation analysis of Klein-Gordon equation with power law nonlinearity. Zbl 1266.34069
Song, Ming; Liu, Zhengrong; Zerrad, Essaid; Biswas, Anjan
2013
Periodic waves and their limits for the Camassa–Holm equation. Zbl 1192.35152
Liu, Zhengrong; Kayed, Ali Mohammed; Chen, Can
2006
Bifurcation sets and distributions of limit cycles in a Hamiltonian system approaching the principal deformation of a $$Z_ 4$$-field. Zbl 0885.58066
Liu, Zhengrong; Hu, Bambi; Li, Jibin
1995
Large time behavior of solutions for density-suppressed motility system in higher dimensions. Zbl 1416.35277
Liu, Zhengrong; Xu, Jiao
2019
Soliton and Riemann theta function quasi-periodic wave solutions for a $$(2+1)$$-dimensional generalized shallow water wave equation. Zbl 1348.76038
Chen, Yiren; Song, Ming; Liu, Zhengrong
2015
Kink-like wave and compacton-like wave solutions for generalized KdV equation. Zbl 1345.37072
Li, Shaoyong; Liu, Zhengrong
2015
Qualitative analysis and explicit traveling wave solutions for the Davey – Stewartson equation. Zbl 1284.35113
Song, Ming; Liu, Zhengrong
2014
Qualitative analysis for a mathematical model of AIDS. Zbl 0790.92019
Jing, Zhujun; Liu, Zhengrong
1993
Boundedness and stabilization in a two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity. Zbl 1415.35044
Jin, Hai-Yang; Liu, Zhengrong; Shi, Shijie; Xu, Jiao
2019
Random traveling wave and bifurcations of asymptotic behaviors in the stochastic KPP equation driven by dual noises. Zbl 1375.35641
Huang, Zhehao; Liu, Zhengrong
2016
The Cauchy problem for a two-component Novikov equation in the critical Besov space. Zbl 1312.35041
Tang, Hao; Liu, Zhengrong
2015
Singular solitons and bifurcation analysis of quadratic nonlinear Klein-Gordon equation. Zbl 1269.35006
Song, Ming; Liu, Zhengrong; Zerrad, Essaid; Biswas, Anjan
2013
Traveling wave solutions for the generalized Zakharov equations. Zbl 1264.35084
Song, Ming; Liu, Zhengrong
2012
Periodic wave solutions and their limits for the generalized KP-BBM equation. Zbl 1255.35183
Song, Ming; Liu, Zhengrong
2012
New exact solutions for mCH and mDP equations by auxiliary equation method. Zbl 1203.35254
Zhang, Bengong; Liu, Zhengrong; Mao, Jianfeng
2010
Persistence of travelling fronts of KdV-Burgers-Kuramoto equation. Zbl 1197.65148
Fu, Yanggeng; Liu, Zhengrong
2010
An estimate for the distance between adjacent zeros of solutions to neutral delay differential equations. Zbl 0962.34050
Zhou, Yong; Liu, Zhengrong; Yu, Yuanhong
1998
Global and local bifurcation in perturbations of non-symmetry and symmetry of Hamiltonian systems. Zbl 0856.34047
Liu, Zhengrong; Jing, Zhujun
1995
Conditions for global stability of the Liénard equation. Zbl 0838.34064
Liu, Zhengrong
1995
Attractors of dissipative soliton equation. Zbl 0811.35117
Tian, Lixin; Xu, Zhenyuan; Liu, Zhengrong
1994
A novel simple hyperchaotic system with two coexisting attractors. Zbl 1434.34024
Yang, Jiaopeng; Liu, Zhengrong
2019
Global dynamics of the Boussinesq-Burgers system with large initial data. Zbl 1352.35006
Jin, Hai-Yang; Liu, Zhengrong
2016
Stochastic traveling wave solution to a stochastic KPP equation. Zbl 1342.60096
Huang, Zhehao; Liu, Zhengrong; Wang, Zhenzhen
2016
Global existence and decay rate of the Boussinesq-Burgers system with large initial data. Zbl 1339.35096
Zhu, Neng; Liu, Zhengrong
2016
Soliton solution and bifurcation analysis of the KP-Benjamin-Bona-Mahoney equation with power law nonlinearity. Zbl 1418.35032
Song, Ming; Liu, Zhengrong; Biswas, Anjan
2015
Traveling wave fronts and minimal wave speed for a delayed non-autonomous Fisher equation without quasimonotonicity. Zbl 1339.35077
Tian, Yanling; Liu, Zhengrong
2015
Stochastic traveling wave solution to stochastic generalized KPP equation. Zbl 1322.60114
Huang, Zhehao; Liu, Zhengrong
2015
Periodic wave solutions and their limits for the ZK-BBM equation. Zbl 1410.35183
Song, Ming; Liu, Zhengrong
2014
Enriched machining feature-based reasoning for generic machining process sequencing. Zbl 1128.90468
Wang, L.; Cai, N.; Feng, H.-Y.; Liu, Z.
2006
Generalized kink waves in a general compressible hyperelastic rod. Zbl 1092.74543
Liu, Zhengrong; Long, Yao
2005
High Reynolds number oscillating contact lines. Zbl 1163.74420
Perlin, M.; Schultz, W. W.; Liu, Z.
2004
Oscillation criteria for second order nonlinear delay difference equations. Zbl 0945.34051
Liu, Zhengrong; Chen, Wendeng; Yu, Yuanhong
1999
On the periodic solutions to a type of differential-iterative equations. Zbl 0992.34052
Ge, Weigao; Liu, Zhengrong; Yu, Yuanhong
1998
Road to chaos for a soft spring system under weak periodic disturbance. Zbl 0584.73072
Liu, Zhengrong; Yao, Weiguo; Zhu, Zhaoxuan
1986
Large time behavior of solutions for the attraction-repulsion Keller-Segel system with large initial data. Zbl 1407.35030
Xu, Jiao; Liu, Zhengrong; Shi, Shijie
2019
The existence and bifurcation of peakon and anti-peakon to the $$n$$-degree $$b$$-equations. Zbl 1388.34043
Yang, Jiaopeng; Li, Zongguang; Liu, Zhengrong
2018
On the Cauchy problem for the Boltzmann equation in Chemin-Lerner type spaces. Zbl 1326.35227
Tang, Hao; Liu, Zhengrong
2016
Orbital stability of peakons for the Degasperis-Procesi equation with strong dispersion. Zbl 1204.35042
Fu, Yanggeng; Liu, Zhengrong; Yang, Xingyu
2010
Image fusion by using steerable pyramid. Zbl 1029.68626
Liu, Z.; Tsukada, K.; Hanasaki, K.; Ho, Y. K.; Dai, Y. P.
2001
A new method for large amplitude sloshing problems. Zbl 0945.76545
Liu, Z.; Huang, Y.
1994
Discontinuous and impulsive excitation. Zbl 0611.70020
Liu, Zhengrong
1987
Chaotic phenomenon in catalytic reaction. Zbl 0658.58019
Liu, Zhengrong; Li, Jibin; Lin, Chang
1986
Explicit decay rates for a generalized Boussinesq-Burgers system. Zbl 1431.35144
Zhu, Neng; Liu, Zhengrong; Wang, Fang; Zhao, Kun
2020
Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026
Liu, Z.; Xu, D. L.; Liao, S. J.
2018
Global dynamics of a quasilinear chemotaxis model arising from tumor invasion. Zbl 1406.35432
Jin, Hai-Yang; Liu, Zhengrong; Shi, Shijie
2018
Global Cauchy problem of a system of parabolic conservation laws arising from a Keller-Segel type chemotaxis model. Zbl 1404.35468
Zhu, Neng; Liu, Zhengrong; Martinez, Vincent R.; Zhao, Kun
2018
On the Boussinesq-Burgers equations driven by dynamic boundary conditions. Zbl 1378.35255
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018
Riemann theta solutions and their asymptotic property for a $$(3+1)$$-dimensional water wave equation. Zbl 1372.35272
Chen, Yiren; Liu, Zhengrong
2017
Asymptotic nonlinear stability of a composite wave of two traveling waves to a chemotaxis model. Zbl 06760569
Shi, Shijie; Liu, Zhengrong
2017
Infinitely many solitary waves of an integrable equation with singularity. Zbl 1351.37247
Pan, Chaohong; Liu, Zhengrong
2016
Two kinds of important bifurcation phenomena of nonlinear waves in a generalized Novikov-Veselov equation. Zbl 1351.35012
Zhu, Neng; Pan, Chaohong; Liu, Zhengrong
2016
Periodic wave solutions and their limits for the modified KdV-KP equations. Zbl 1329.34083
Song, Ming; Liu, Zheng Rong; Yang, Chen Xi
2015
Some new nonlinear wave solutions and their convergence for the $$(2+1)$$-dimensional Broer-Kau-Kupershmidt equation. Zbl 1320.35131
Yan, Weifang; Liu, Zhengrong
2015
The traveling wave solutions and their bifurcations for the BBM-like $$B(m,n)$$ equations. Zbl 1397.35256
Li, Shaoyong; Liu, Zhengrong
2013
The bifurcations of traveling wave solutions of the Kundu equation. Zbl 1397.35292
Yi, Yating; Liu, Zhengrong
2013
New types of nonlinear waves and bifurcation phenomena in Schamel-Korteweg-de Vries equation. Zbl 1293.35032
Wu, Yun; Liu, Zhengrong
2013
Further results on the traveling wave solutions for an integrable equation. Zbl 1266.37032
Pan, Chaohong; Liu, Zhengrong
2013
A simple approach for reducing the order of equations with higher order nonlinearity. Zbl 1245.35012
Pan, Chao-Hong; Zhu, Xue-Na; Liu, Zheng-Rong
2012
Non-uniform dependence on initial data for the periodic Degasperis-Procesi equation. Zbl 1235.35244
Fu, Yanggeng; Liu, Zhengrong
2011
A simple method and its applications to nonlinear partial differential equations. Zbl 1205.35269
Pan, Chaohong; Liu, Zhengrong; Zhang, Bengong
2010
Explicit decay rates for a generalized Boussinesq-Burgers system. Zbl 1431.35144
Zhu, Neng; Liu, Zhengrong; Wang, Fang; Zhao, Kun
2020
Large time behavior of solutions for density-suppressed motility system in higher dimensions. Zbl 1416.35277
Liu, Zhengrong; Xu, Jiao
2019
Boundedness and stabilization in a two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity. Zbl 1415.35044
Jin, Hai-Yang; Liu, Zhengrong; Shi, Shijie; Xu, Jiao
2019
A novel simple hyperchaotic system with two coexisting attractors. Zbl 1434.34024
Yang, Jiaopeng; Liu, Zhengrong
2019
Large time behavior of solutions for the attraction-repulsion Keller-Segel system with large initial data. Zbl 1407.35030
Xu, Jiao; Liu, Zhengrong; Shi, Shijie
2019
The existence and bifurcation of peakon and anti-peakon to the $$n$$-degree $$b$$-equations. Zbl 1388.34043
Yang, Jiaopeng; Li, Zongguang; Liu, Zhengrong
2018
Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026
Liu, Z.; Xu, D. L.; Liao, S. J.
2018
Global dynamics of a quasilinear chemotaxis model arising from tumor invasion. Zbl 1406.35432
Jin, Hai-Yang; Liu, Zhengrong; Shi, Shijie
2018
Global Cauchy problem of a system of parabolic conservation laws arising from a Keller-Segel type chemotaxis model. Zbl 1404.35468
Zhu, Neng; Liu, Zhengrong; Martinez, Vincent R.; Zhao, Kun
2018
On the Boussinesq-Burgers equations driven by dynamic boundary conditions. Zbl 1378.35255
Zhu, Neng; Liu, Zhengrong; Zhao, Kun
2018
Boundedness and large time behavior of an attraction-repulsion chemotaxis model with logistic source. Zbl 1357.35050
Shi, Shijie; Liu, Zhengrong; Jin, Hai-Yang
2017
Riemann theta solutions and their asymptotic property for a $$(3+1)$$-dimensional water wave equation. Zbl 1372.35272
Chen, Yiren; Liu, Zhengrong
2017
Asymptotic nonlinear stability of a composite wave of two traveling waves to a chemotaxis model. Zbl 06760569
Shi, Shijie; Liu, Zhengrong
2017
Random traveling wave and bifurcations of asymptotic behaviors in the stochastic KPP equation driven by dual noises. Zbl 1375.35641
Huang, Zhehao; Liu, Zhengrong
2016
Global dynamics of the Boussinesq-Burgers system with large initial data. Zbl 1352.35006
Jin, Hai-Yang; Liu, Zhengrong
2016
Stochastic traveling wave solution to a stochastic KPP equation. Zbl 1342.60096
Huang, Zhehao; Liu, Zhengrong; Wang, Zhenzhen
2016
Global existence and decay rate of the Boussinesq-Burgers system with large initial data. Zbl 1339.35096
Zhu, Neng; Liu, Zhengrong
2016
On the Cauchy problem for the Boltzmann equation in Chemin-Lerner type spaces. Zbl 1326.35227
Tang, Hao; Liu, Zhengrong
2016
Infinitely many solitary waves of an integrable equation with singularity. Zbl 1351.37247
Pan, Chaohong; Liu, Zhengrong
2016
Two kinds of important bifurcation phenomena of nonlinear waves in a generalized Novikov-Veselov equation. Zbl 1351.35012
Zhu, Neng; Pan, Chaohong; Liu, Zhengrong
2016
Large time behavior of the full attraction-repulsion Keller-Segel system in the whole space. Zbl 1326.35042
Jin, Hai-Yang; Liu, Zhengrong
2015
Well-posedness of the modified Camassa-Holm equation in Besov spaces. Zbl 1327.35345
Tang, Hao; Liu, Zhengrong
2015
The dependences on initial data for the b-family equation in critical Besov space. Zbl 1319.35227
Tang, Hao; Shi, Shijie; Liu, Zhengrong
2015
Soliton and Riemann theta function quasi-periodic wave solutions for a $$(2+1)$$-dimensional generalized shallow water wave equation. Zbl 1348.76038
Chen, Yiren; Song, Ming; Liu, Zhengrong
2015
Kink-like wave and compacton-like wave solutions for generalized KdV equation. Zbl 1345.37072
Li, Shaoyong; Liu, Zhengrong
2015
The Cauchy problem for a two-component Novikov equation in the critical Besov space. Zbl 1312.35041
Tang, Hao; Liu, Zhengrong
2015
Soliton solution and bifurcation analysis of the KP-Benjamin-Bona-Mahoney equation with power law nonlinearity. Zbl 1418.35032
Song, Ming; Liu, Zhengrong; Biswas, Anjan
2015
Traveling wave fronts and minimal wave speed for a delayed non-autonomous Fisher equation without quasimonotonicity. Zbl 1339.35077
Tian, Yanling; Liu, Zhengrong
2015
Stochastic traveling wave solution to stochastic generalized KPP equation. Zbl 1322.60114
Huang, Zhehao; Liu, Zhengrong
2015
Periodic wave solutions and their limits for the modified KdV-KP equations. Zbl 1329.34083
Song, Ming; Liu, Zheng Rong; Yang, Chen Xi
2015
Some new nonlinear wave solutions and their convergence for the $$(2+1)$$-dimensional Broer-Kau-Kupershmidt equation. Zbl 1320.35131
Yan, Weifang; Liu, Zhengrong
2015
A note on the solution map for the periodic Camassa-Holm equation. Zbl 1310.35078
Tang, Hao; Zhao, Yongye; Liu, Zhengrong
2014
Continuous properties of the solution map for the Euler equations. Zbl 1293.35229
Tang, Hao; Liu, Zhengrong
2014
Qualitative analysis and explicit traveling wave solutions for the Davey – Stewartson equation. Zbl 1284.35113
Song, Ming; Liu, Zhengrong
2014
Periodic wave solutions and their limits for the ZK-BBM equation. Zbl 1410.35183
Song, Ming; Liu, Zhengrong
2014
Non-uniform dependence on initial data for the periodic modified Camassa-Holm equation. Zbl 1268.35011
Fu, Yanggeng; Liu, Zhengrong
2013
Singular soliton solution and bifurcation analysis of Klein-Gordon equation with power law nonlinearity. Zbl 1266.34069
Song, Ming; Liu, Zhengrong; Zerrad, Essaid; Biswas, Anjan
2013
Singular solitons and bifurcation analysis of quadratic nonlinear Klein-Gordon equation. Zbl 1269.35006
Song, Ming; Liu, Zhengrong; Zerrad, Essaid; Biswas, Anjan
2013
The traveling wave solutions and their bifurcations for the BBM-like $$B(m,n)$$ equations. Zbl 1397.35256
Li, Shaoyong; Liu, Zhengrong
2013
The bifurcations of traveling wave solutions of the Kundu equation. Zbl 1397.35292
Yi, Yating; Liu, Zhengrong
2013
New types of nonlinear waves and bifurcation phenomena in Schamel-Korteweg-de Vries equation. Zbl 1293.35032
Wu, Yun; Liu, Zhengrong
2013
Further results on the traveling wave solutions for an integrable equation. Zbl 1266.37032
Pan, Chaohong; Liu, Zhengrong
2013
Traveling wave solutions for the generalized Zakharov equations. Zbl 1264.35084
Song, Ming; Liu, Zhengrong
2012
Periodic wave solutions and their limits for the generalized KP-BBM equation. Zbl 1255.35183
Song, Ming; Liu, Zhengrong
2012
A simple approach for reducing the order of equations with higher order nonlinearity. Zbl 1245.35012
Pan, Chao-Hong; Zhu, Xue-Na; Liu, Zheng-Rong
2012
Bifurcation of peakons and periodic cusp waves for the generalization of the Camassa-Holm equation. Zbl 1218.35026
Wen, Zhenshu; Liu, Zhengrong
2011
The explicit nonlinear wave solutions and their bifurcations of the generalized Camassa-Holm equation. Zbl 1258.35050
Liu, Zhengrong; Liang, Yong
2011
Non-uniform dependence on initial data for the periodic Degasperis-Procesi equation. Zbl 1235.35244
Fu, Yanggeng; Liu, Zhengrong
2011
New exact solitary wave and multiple soliton solutions of quantum Zakharov-Kuznetsov equation. Zbl 1200.35238
Zhang, Bengong; Liu, Zhengrong; Xiao, Qing
2010
Explicit periodic wave solutions and their bifurcations for generalized Camassa – Holm equation. Zbl 1202.35048
Liu, Zhengrong; Tang, Hao
2010
New exact solutions for mCH and mDP equations by auxiliary equation method. Zbl 1203.35254
Zhang, Bengong; Liu, Zhengrong; Mao, Jianfeng
2010
Persistence of travelling fronts of KdV-Burgers-Kuramoto equation. Zbl 1197.65148
Fu, Yanggeng; Liu, Zhengrong
2010
Orbital stability of peakons for the Degasperis-Procesi equation with strong dispersion. Zbl 1204.35042
Fu, Yanggeng; Liu, Zhengrong; Yang, Xingyu
2010
A simple method and its applications to nonlinear partial differential equations. Zbl 1205.35269
Pan, Chaohong; Liu, Zhengrong; Zhang, Bengong
2010
New exact solutions for the classical Drinfel’d-Sokolov-Wilson equation. Zbl 1181.35221
Wen, Zhenshu; Liu, Zhengrong; Song, Ming
2009
Coexistence of multifarious explicit nonlinear wave solutions for modified forms of Camassa-Holm and Degaperis-Procesi equations. Zbl 1176.34005
Liu, Zhengrong; Pan, Jian
2009
Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations. Zbl 1220.34010
Zhang, Ben-Gong; Li, Shao-Yong; Liu, Zheng-Rong
2008
Orbital stability of peakons with nonvanishing boundary for CH and CH-$$\gamma$$ equations. Zbl 1227.34018
Ouyang, Zheng-Yong; Zheng, Shan; Liu, Zheng-Rong
2008
A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations. Zbl 1203.35234
Liu, Zhengrong; Ouyang, Zhengyong
2007
Compacton-like wave and kink-like wave of GCH equation. Zbl 1106.35065
Liu, Zhengrong; Long, Yao
2007
Periodic waves and their limits for the Camassa–Holm equation. Zbl 1192.35152
Liu, Zhengrong; Kayed, Ali Mohammed; Chen, Can
2006
Enriched machining feature-based reasoning for generic machining process sequencing. Zbl 1128.90468
Wang, L.; Cai, N.; Feng, H.-Y.; Liu, Z.
2006
Periodic cusp wave solutions and single-solitons for the $$b$$-equation. Zbl 1068.35103
Guo, Boling; Liu, Zhengrong
2005
Two new types of bounded waves of CH-$$\gamma$$ equation. Zbl 1217.35161
Guo, Boling; Liu, Zhengrong
2005
Generalized kink waves in a general compressible hyperelastic rod. Zbl 1092.74543
Liu, Zhengrong; Long, Yao
2005
Modelling chemo-hydro-mechanical behaviour of unsaturated clays: a feasibility study. Zbl 1105.74304
Liu, Z.; Boukpeti, Nathalie; Li, X.; Collin, F.; Radu, J.-P.; Hueckel, T.; Charlier, R.
2005
Peaked wave solutions of Camassa-Holm equation. Zbl 1068.35136
Liu, Zhengrong; Wang, Ruiqi; Jing, Zhujun
2004
New bounded traveling waves of Camassa-Holm equation. Zbl 1063.35138
Liu, Zhengrong; Li, Qixiu; Lin, Qingmei
2004
Compactons in a general compressible hyperelastic rod. Zbl 1116.74374
Liu, Zhengrong; Chen, Can
2004
Integral approach to compacton solutions of Boussinesq-like $$B$$($$m$$,$$n$$) equation with fully nonlinear dispersion. Zbl 1068.35135
Liu, Zhengrong; Lin, Qingmei; Li, Qixiu
2004
High Reynolds number oscillating contact lines. Zbl 1163.74420
Perlin, M.; Schultz, W. W.; Liu, Z.
2004
Peaked wave solutions of CH-r equation. Zbl 1089.35521
Guo, Boling; Liu, Zhengrong
2003
The same distribution of limit cycles in five perturbed cubic Hamiltonian systems. Zbl 1074.34040
Liu, Zhengrong; Yang, Zhiyan; Jiang, Tao
2003
Traveling wave solutions for a class of nonlinear dispersive equations. Zbl 1011.35014
Li, Jibin; Liu, Zhengrong
2002
Peakons of the Camassa-Holm equation. Zbl 1018.35061
Liu, Zhengrong; Qian, Tifei
2002
The application of bifurcation method to a higher-order KdV equation. Zbl 1012.35076
Liu, Zhengrong; Yang, Chenxi
2002
Bifurcations of solitary waves and domain wall waves for KdV-like equation with higher order nonlinearity. Zbl 1042.35067
Liu, Zhengrong; Li, Jibin
2002
Detection function method and its application to a perturbed quintic Hamiltonian system. Zbl 0994.37022
Liu, Zhengrong; Qian, Tifei; Li, Jibin
2002
Bifurcation set and distribution of limit cycles for a class of seven-order Hamiltonian system with fifteen-order perturbed terms. Zbl 0994.37024
Wang, Ruiqi; Liu, Zhengrong; Jing, Zhujun
2002
On the reflection function and the periodic solution of second-order quadratic differential systems. Zbl 1049.34510
Zhou, Zhengxin; Liu, Zhengrong; Yan, Yuexin; Yu, Yuanhong
2002
Peakons and their bifurcation in a generalized Camassa-Holm equation. Zbl 1090.37554
Liu, Zhengrong; Qian, Tifei
2001
Large-scale modes of turbulent channel flow: transport and structure. Zbl 1102.76314
Liu, Z.; Adrian, R. J.; Hanratty, T. J.
2001
Image fusion by using steerable pyramid. Zbl 1029.68626
Liu, Z.; Tsukada, K.; Hanasaki, K.; Ho, Y. K.; Dai, Y. P.
2001
Oscillation theorems for hyperbolic equations of neutral type. Zbl 1027.35148
Luo, Jiaowan; Liu, Zhengrong; Yu, Yuanhong
2001
Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. Zbl 0985.37072
Li, Jibin; Liu, Zhengrong
2000
Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms. Zbl 0974.34038
Cao, Hongjun; Liu, Zhengrong; Jing, Zhujun
2000
Hamiltonian symmetric groups and multiple periodic solutions to delay differential equations. Zbl 0920.34061
Li, Jibin; He, Xue-Zhong; Liu, Zhengrong
1999
Periodic solutions to some differential delay equations created by Hamiltonian systems. Zbl 0946.34063
Li, Jibin; Liu, Zhengrong; He, Xuezhong
1999
Oscillation criteria for second order nonlinear delay difference equations. Zbl 0945.34051
Liu, Zhengrong; Chen, Wendeng; Yu, Yuanhong
1999
On the connection between two parts of Hilbert’s 16th problem and equivariant bifurcation problem. Zbl 0967.34025
Li, Jibin; Liu, Zhengrong
1998
An estimate for the distance between adjacent zeros of solutions to neutral delay differential equations. Zbl 0962.34050
Zhou, Yong; Liu, Zhengrong; Yu, Yuanhong
1998
On the periodic solutions to a type of differential-iterative equations. Zbl 0992.34052
Ge, Weigao; Liu, Zhengrong; Yu, Yuanhong
1998
An analysis of the distortion and breakup mechanisms of high speed liquid drops. Zbl 1135.76481
Liu, Z.; Reitz, R. D.
1997
Oscillation of solutions of nonlinear partial differential equations of neutral type. Zbl 0909.35010
Yu, Yuanhong; Liu, Bin; Liu, Zhengrong
1997
Chaotic oscillation of saddle form cable-suspended roofs under vertical excitation action. Zbl 0878.73033
Fan, Jiashen; He, Fusheng; Liu, Zhengrong
1997
Nonoscillatory solutions of second order functional differential equations. Zbl 0876.34076
Liu, Zhengrong; Yu, Yuanhong
1997
On oscillation and nonoscillation of a class of nonlinear differential equations. Zbl 0898.34031
Liu, Zhengrong; Yu, Yuanhong
1996
Bifurcation sets and distributions of limit cycles in a Hamiltonian system approaching the principal deformation of a $$Z_ 4$$-field. Zbl 0885.58066
Liu, Zhengrong; Hu, Bambi; Li, Jibin
1995
Global and local bifurcation in perturbations of non-symmetry and symmetry of Hamiltonian systems. Zbl 0856.34047
Liu, Zhengrong; Jing, Zhujun
1995
Conditions for global stability of the Liénard equation. Zbl 0838.34064
Liu, Zhengrong
1995
...and 10 more Documents
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#### Cited by 807 Authors

 53 Liu, Zhengrong 38 Li, Jibin 27 Tang, Shengqiang 25 Tian, Lixin 22 He, Bin 22 Song, Ming 19 Rui, Weiguo 18 Han, Maoan 18 Long, Yao 14 Huang, Wentao 14 Shen, Jianwei 13 Wen, Zhenshu 12 Chen, Aiyong 11 Wu, Yuhai 10 Zhang, Lijun 9 Chen, Can 9 Meng, Qing 9 Pan, Chaohong 9 Xu, Wei 8 Tang, Hao 8 Zhou, Hongxian 7 Biswas, Anjan 7 Cheng, Rong 7 Li, Shaoyong 7 Liu, Qian 7 Liu, Rui 7 Yin, Jiuli 7 Zhang, Bengong 7 Zhao, Xiaoshan 7 Zhou, Yuqian 6 Chen, Guanrong 6 Fan, Xinghua 6 Geng, Yixiang 6 Guo, Zhiming 6 Mu, Chunlai 6 Ouyang, Zhengyong 6 Tang, Minying 6 Wu, Yonghong 6 Xu, Wei 6 Yuan, Wenjun 6 Zhou, Jiangbo 5 Bi, Qinsheng 5 Chen, Liqun 5 Deng, Xijun 5 He, Tianlan 5 Jing, Zhujun 5 Tunç, Cemil 5 Wang, Zhaojuan 5 Wazwaz, Abdul-Majid Abdul-Rahman 5 Xie, Shaolong 5 Yang, Chenxi 5 Yu, Jian-She 5 Zang, Hong 5 Zhang, Kelei 5 Zhang, Tonghua 5 Zhang, Weiguo 5 Zhu, Neng 5 Zhu, Wenjing 4 Chen, Yiren 4 Feng, Dahe 4 Ge, Weigao 4 Huo, Xuwen 4 Jin, Hai-Yang 4 Li, Shumin 4 Li, Zhenyang 4 Tang, Yaning 4 Wang, Xiaohuan 4 Wang, Zhian 4 Wu, Yun 4 Xie, Yongan 4 Yin, Zhaoyang 4 Zhang, Weinian 4 Zhao, Kun 4 Zhou, Shouming 3 Adrian, Ronald J. 3 Bai, Yuzhen 3 Cai, Jionghui 3 Cao, Jun 3 Du, Zengji 3 Feng, Hsi-Yung 3 Guo, Boling 3 Jia, Huabing 3 Khalique, Chaudry Masood 3 Lai, Shaoyong 3 Li, Li 3 Li, Shaolin 3 Li, Yin 3 Liu, Zengrong 3 Llibre, Jaume 3 Lv, Wenbin 3 Meng, Fanning 3 Qiao, Lijing 3 Qiao, Zhijun 3 Ren, Guoqiang 3 Saker, Samir H. 3 Sung, Hyung Jin 3 Tarţa, Alexandrina-Alina 3 Wang, Fang 3 Wang, Lihui 3 Wang, Ruiqi ...and 707 more Authors
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#### Cited in 121 Serials

 96 Applied Mathematics and Computation 51 Chaos, Solitons and Fractals 35 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 31 Nonlinear Dynamics 28 Nonlinear Analysis. Real World Applications 23 Abstract and Applied Analysis 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 Communications in Nonlinear Science and Numerical Simulation 15 Journal of Mathematical Analysis and Applications 14 Journal of Fluid Mechanics 13 Computers & Mathematics with Applications 12 Journal of Differential Equations 12 Applied Mathematics and Mechanics. (English Edition) 12 Mathematical Problems in Engineering 12 Journal of Applied Analysis and Computation 10 Advances in Difference Equations 9 Mathematical Methods in the Applied Sciences 9 Acta Mathematicae Applicatae Sinica. English Series 9 Advances in Mathematical Physics 7 Applicable Analysis 7 Applied Mathematics Letters 7 Physics of Fluids 7 Journal of Applied Mathematics 6 Acta Mathematica Sinica. English Series 6 Journal of Nonlinear Mathematical Physics 5 Journal of Mathematical Physics 5 NoDEA. Nonlinear Differential Equations and Applications 4 Computers and Fluids 4 Journal of Computational Physics 4 Journal of Computational and Applied Mathematics 4 Acta Applicandae Mathematicae 4 Science in China. Series A 4 Discrete and Continuous Dynamical Systems 4 Journal of Applied Mathematics and Computing 4 Journal of Function Spaces 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 International Journal of Production Research 3 Mathematical and Computer Modelling 3 Applied Mathematical Modelling 3 International Journal of Computer Mathematics 3 International Journal of Numerical Methods for Heat & Fluid Flow 3 Discrete Dynamics in Nature and Society 3 Waves in Random and Complex Media 2 Reports on Mathematical Physics 2 Physica D 2 Numerical Methods for Partial Differential Equations 2 Journal of Dynamics and Differential Equations 2 Journal of Nonlinear Science 2 Applied Mathematics. Series B (English Edition) 2 Engineering Analysis with Boundary Elements 2 Journal of Inequalities and Applications 2 Chaos 2 European Journal of Mechanics. B. Fluids 2 Flow, Turbulence and Combustion 2 Nonlinear Analysis. Modelling and Control 2 Discrete and Continuous Dynamical Systems. Series B 2 Stochastics and Dynamics 2 Boundary Value Problems 2 Kinetic and Related Models 2 International Journal of Differential Equations 2 Science China. Mathematics 2 Afrika Matematika 1 Acta Mechanica 1 Astrophysics and Space Science 1 Biological Cybernetics 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 International Journal for Numerical Methods in Fluids 1 Indian Journal of Pure & Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Applied Mathematics and Mechanics 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Mathematical Notes 1 Nonlinearity 1 Physica A 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Wave Motion 1 Bulletin of the London Mathematical Society 1 Czechoslovak Mathematical Journal 1 Mathematics and Computers in Simulation 1 Meccanica 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 Ricerche di Matematica 1 Siberian Mathematical Journal 1 Studies in Applied Mathematics 1 Applied Numerical Mathematics 1 Computational Mathematics and Mathematical Physics 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Acta Mechanica Sinica. (English Edition) 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of the Egyptian Mathematical Society 1 Bulletin des Sciences Mathématiques 1 Advances in Differential Equations 1 Electronic Journal of Probability 1 Journal of Vibration and Control ...and 21 more Serials
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#### Cited in 32 Fields

 445 Partial differential equations (35-XX) 192 Dynamical systems and ergodic theory (37-XX) 163 Ordinary differential equations (34-XX) 93 Fluid mechanics (76-XX) 34 Biology and other natural sciences (92-XX) 28 Numerical analysis (65-XX) 22 Global analysis, analysis on manifolds (58-XX) 18 Mechanics of deformable solids (74-XX) 11 Operator theory (47-XX) 11 Mechanics of particles and systems (70-XX) 8 Difference and functional equations (39-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Functions of a complex variable (30-XX) 6 Probability theory and stochastic processes (60-XX) 5 Quantum theory (81-XX) 5 Systems theory; control (93-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Operations research, mathematical programming (90-XX) 3 Real functions (26-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX)