Shen, Yuan; Tian, Bo; Yang, Dan-Yu; Zhou, Tian-Yu Studies on a three-field lattice system: \(N\)-fold Darboux transformation, conservation laws and analytic solutions. (English) Zbl 1511.35306 Qual. Theory Dyn. Syst. 22, No. 2, Paper No. 74, 15 p. (2023). MSC: 35Q51 35C08 37K10 37K40 37K60 37K35 PDFBibTeX XMLCite \textit{Y. Shen} et al., Qual. Theory Dyn. Syst. 22, No. 2, Paper No. 74, 15 p. (2023; Zbl 1511.35306) Full Text: DOI
Shen, Yuan; Tian, Bo; Zhou, Tian-Yu; Gao, Xiao-Tian Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions. (English) Zbl 1508.35159 Chaos Solitons Fractals 164, Article ID 112460, 7 p. (2022). MSC: 35Q55 37K10 37K35 37K40 PDFBibTeX XMLCite \textit{Y. Shen} et al., Chaos Solitons Fractals 164, Article ID 112460, 7 p. (2022; Zbl 1508.35159) Full Text: DOI
Yin, Hui-Min; Tian, Bo; Hu, Cong-Cong; Zhao, Xin-Chao Chaotic motions for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a nano optical fiber. (English) Zbl 1414.35215 Appl. Math. Lett. 93, 139-146 (2019). MSC: 35Q55 78A60 35B20 37K10 PDFBibTeX XMLCite \textit{H.-M. Yin} et al., Appl. Math. Lett. 93, 139--146 (2019; Zbl 1414.35215) Full Text: DOI
Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials. (English) Zbl 1514.35409 Physica A 492, 524-533 (2018). MSC: 35Q55 37K10 PDFBibTeX XMLCite \textit{L. Liu} et al., Physica A 492, 524--533 (2018; Zbl 1514.35409) Full Text: DOI
Sun, Ya; Tian, Bo; Wang, Yu-Feng; Zhen, Hui-Ling Bäcklund transformation and \(N\)-shock-wave solutions for a (3+1)-dimensional nonlinear evolution equation. (English) Zbl 1354.37071 Nonlinear Dyn. 84, No. 2, 851-861 (2016). MSC: 37K35 37K10 76L05 PDFBibTeX XMLCite \textit{Y. Sun} et al., Nonlinear Dyn. 84, No. 2, 851--861 (2016; Zbl 1354.37071) Full Text: DOI
Wang, Yun-Po; Tian, Bo; Wang, Ming; Wang, Yu-Feng; Sun, Ya; Xie, Xi-Yang Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves. (English) Zbl 1348.37108 Nonlinear Dyn. 81, No. 4, 1815-1821 (2015). MSC: 37K10 35Q35 76B15 PDFBibTeX XMLCite \textit{Y.-P. Wang} et al., Nonlinear Dyn. 81, No. 4, 1815--1821 (2015; Zbl 1348.37108) Full Text: DOI
Huang, Zhi-Ruo; Tian, Bo; Zhen, Hui-Ling; Jiang, Yan; Wang, Yun-po; Sun, Ya Bäcklund transformations and soliton solutions for a \((3+1)\)-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics. (English) Zbl 1345.37070 Nonlinear Dyn. 80, No. 1-2, 1-7 (2015). MSC: 37K10 76B15 37N10 35C08 35Q35 35Q53 PDFBibTeX XMLCite \textit{Z.-R. Huang} et al., Nonlinear Dyn. 80, No. 1--2, 1--7 (2015; Zbl 1345.37070) Full Text: DOI
Liu, De-Yin; Tian, Bo; Jiang, Yan; Sun, Wen-Rong Soliton solutions and Bäcklund transformations of a (2+1)-dimensional nonlinear evolution equation via the Jaulent-Miodek hierarchy. (English) Zbl 1331.37092 Nonlinear Dyn. 78, No. 4, 2341-2347 (2014). MSC: 37K10 35C08 PDFBibTeX XMLCite \textit{D.-Y. Liu} et al., Nonlinear Dyn. 78, No. 4, 2341--2347 (2014; Zbl 1331.37092) Full Text: DOI
Wang, Pan; Tian, Bo; Liu, Wen-Jun; Sun, Kun \(N\)-soliton solutions, Bäcklund transformation and conservation laws for the integro-differential nonlinear Schrödinger equation from the isotropic inhomogeneous Heisenberg spin magnetic chain. (Russian, English) Zbl 1313.35329 Zh. Vychisl. Mat. Mat. Fiz. 54, No. 4, 720-720 (2014); translation in Comput. Math. Math. Phys. 54, No. 4, 727-743 (2014). MSC: 35Q55 37K10 PDFBibTeX XMLCite \textit{P. Wang} et al., Zh. Vychisl. Mat. Mat. Fiz. 54, No. 4, 720--720 (2014; Zbl 1313.35329); translation in Comput. Math. Math. Phys. 54, No. 4, 727--743 (2014) Full Text: DOI
Zhou, Hui-Ping; Tian, Bo; Mo, Hui-Xia; Li, Min; Wang, Pan Bäcklund transformation, Lax pair and solitons of the \((2+1)\)-dimensional Davey-Stewartson-like equations with variable coefficients for the electrostatic wave packets. (English) Zbl 1420.35336 J. Nonlinear Math. Phys. 20, No. 1, 94-105 (2013). MSC: 35Q53 35Q55 37K10 PDFBibTeX XMLCite \textit{H.-P. Zhou} et al., J. Nonlinear Math. Phys. 20, No. 1, 94--105 (2013; Zbl 1420.35336) Full Text: DOI
Wang, Ming; Shan, Wen-Rui; Lü, Xing; Xue, Yu-Shan; Lin, Zhi-Qiang; Tian, Bo Soliton collision in a general coupled nonlinear Schrödinger system via symbolic computation. (English) Zbl 1311.35299 Appl. Math. Comput. 219, No. 24, 11258-11264 (2013). MSC: 35Q55 68W30 35C08 78A60 37K10 PDFBibTeX XMLCite \textit{M. Wang} et al., Appl. Math. Comput. 219, No. 24, 11258--11264 (2013; Zbl 1311.35299) Full Text: DOI
Wang, Yu-Feng; Tian, Bo; Wang, Ming Bell-polynomial approach and integrability for the coupled Gross-Pitaevskii equations in Bose-Einstein condensates. (English) Zbl 1338.37095 Stud. Appl. Math. 131, No. 2, 119-134 (2013). MSC: 37K10 35C08 37N20 37M05 PDFBibTeX XMLCite \textit{Y.-F. Wang} et al., Stud. Appl. Math. 131, No. 2, 119--134 (2013; Zbl 1338.37095) Full Text: DOI
Li, Min; Xiao, Jing-Hua; Yan, Tian-Zhong; Tian, Bo Integrability and soliton interaction of a resonant nonlinear Schrödinger equation via binary Bell polynomials. (English) Zbl 1270.37046 Nonlinear Anal., Real World Appl. 14, No. 3, 1669-1679 (2013). MSC: 37K10 37K35 35C08 35Q55 11B73 33C47 PDFBibTeX XMLCite \textit{M. Li} et al., Nonlinear Anal., Real World Appl. 14, No. 3, 1669--1679 (2013; Zbl 1270.37046) Full Text: DOI
Lü, Xing; Tian, Bo; Qi, Feng Hua Bell-polynomial construction of Bäcklund transformations with auxiliary independent variable for some soliton equations with one tau-function. (English) Zbl 1239.35132 Nonlinear Anal., Real World Appl. 13, No. 3, 1130-1138 (2012). MSC: 35Q51 37K10 35Q53 68W30 PDFBibTeX XMLCite \textit{X. Lü} et al., Nonlinear Anal., Real World Appl. 13, No. 3, 1130--1138 (2012; Zbl 1239.35132) Full Text: DOI
Qu, Qi-Xing; Tian, Bo; Sun, Kun; Jiang, Yan Bäcklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation. (English) Zbl 1314.37050 J. Math. Phys. 52, No. 1, 013511, 10 p. (2011). MSC: 37K10 37K15 37K35 35C08 33E10 PDFBibTeX XMLCite \textit{Q.-X. Qu} et al., J. Math. Phys. 52, No. 1, 013511, 10 p. (2011; Zbl 1314.37050) Full Text: DOI
Zhu, Hong-Wu; Tian, Bo; Zhang, Chun-Yi On the existence of infinite conservation laws of a variable-coefficient Korteweg-de Vries model with symbolic computation. (English) Zbl 1260.37042 Mod. Phys. Lett. B 25, No. 20, 1683-1689 (2011). MSC: 37K15 35Q53 37K05 37K10 PDFBibTeX XMLCite \textit{H.-W. Zhu} et al., Mod. Phys. Lett. B 25, No. 20, 1683--1689 (2011; Zbl 1260.37042) Full Text: DOI
Qin, Bo; Tian, Bo; Liu, Wen-Jun; Liu, Li-Cai; Qu, Qi-Xing; Zhang, Hai-Qiang Solitonic excitations and interactions in the three-spine \(\alpha\)-helical protein with inhomogeneity. (English) Zbl 1232.35159 SIAM J. Appl. Math. 71, No. 4, 1317-1353 (2011). MSC: 35Q55 35Q51 37J35 68W30 92B05 PDFBibTeX XMLCite \textit{B. Qin} et al., SIAM J. Appl. Math. 71, No. 4, 1317--1353 (2011; Zbl 1232.35159) Full Text: DOI
Lü, Xing; Tian, Bo; Sun, Kun; Wang, Pan Bell-polynomial manipulations on the Bäcklund transformations and Lax pairs for some soliton equations with one Tau-function. (English) Zbl 1314.35129 J. Math. Phys. 51, No. 11, 113506, 8 p. (2010). MSC: 35Q51 37K10 37K35 35C11 PDFBibTeX XMLCite \textit{X. Lü} et al., J. Math. Phys. 51, No. 11, 113506, 8 p. (2010; Zbl 1314.35129) Full Text: DOI
Lü, Xing; Tian, Bo; Zhang, Hai-Qiang; Xu, Tao; Li, He Integrability study on a generalized \((2+1)\)-dimensional variable-coefficient gardner model with symbolic computation. (English) Zbl 1311.35261 Chaos 20, No. 4, 043125, 4 p. (2010). MSC: 35Q53 37K10 37K35 68W30 PDFBibTeX XMLCite \textit{X. Lü} et al., Chaos 20, No. 4, 043125, 4 p. (2010; Zbl 1311.35261) Full Text: DOI
Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Li, Min; Wang, Pan; Sun, Kun Solitons, Bäcklund transformation, and Lax pair for the \((2+1)\)-dimensional Boiti-Leon-Pempinelli equation for the water waves. (English) Zbl 1309.76036 J. Math. Phys. 51, No. 9, 093519, 11 p. (2010). MSC: 76B15 76B25 76L05 37K10 37K35 37K40 PDFBibTeX XMLCite \textit{Y. Jiang} et al., J. Math. Phys. 51, No. 9, 093519, 11 p. (2010; Zbl 1309.76036) Full Text: DOI
Sun, Kun; Tian, Bo; Liu, Wen-Jun; Li, Min; Qu, Qi-Xing; Jiang, Yan Symbolic-computation study on the (2+1)-dimensional dispersive long wave system. (English) Zbl 1385.76007 SIAM J. Appl. Math. 70, No. 7, 2259-2272 (2010). MSC: 76B25 35Q35 68W30 74J20 37J35 PDFBibTeX XMLCite \textit{K. Sun} et al., SIAM J. Appl. Math. 70, No. 7, 2259--2272 (2010; Zbl 1385.76007) Full Text: DOI
Qu, Qi-Xing; Tian, Bo; Liu, Wen-Jun; Li, Min; Sun, Kun Painlevé integrability and \(N\)-soliton solution for the variable-coefficient Zakharov-Kuznetsov equation from plasmas. (English) Zbl 1207.35091 Nonlinear Dyn. 62, No. 1-2, 229-235 (2010). MSC: 35C08 82D10 35Q60 37K10 35Q51 PDFBibTeX XMLCite \textit{Q.-X. Qu} et al., Nonlinear Dyn. 62, No. 1--2, 229--235 (2010; Zbl 1207.35091) Full Text: DOI
Geng, Tao; Meng, Xiang-Hua; Shan, Wen-Rui; Tian, Bo Bäcklund transformation and multi-soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries system via symbolic computation. (English) Zbl 1203.35218 Appl. Math. Comput. 217, No. 4, 1470-1475 (2010). MSC: 35Q53 35-04 35C08 35A24 37K10 37K35 PDFBibTeX XMLCite \textit{T. Geng} et al., Appl. Math. Comput. 217, No. 4, 1470--1475 (2010; Zbl 1203.35218) Full Text: DOI
Li, Juan; Tian, Bo; Wei, Guang-Mei; Zhang, Hai-Qiang Integrable properties and similarity reductions of the sine-Laplace equation from an inviscid incompressible fluid with symbolic computation. (English) Zbl 1203.37109 Int. J. Mod. Phys. B 24, No. 9, 1173-1185 (2010). Reviewer: Rakib Efendiev (Baku) MSC: 37K10 37K35 37K30 68W30 76B25 34M55 PDFBibTeX XMLCite \textit{J. Li} et al., Int. J. Mod. Phys. B 24, No. 9, 1173--1185 (2010; Zbl 1203.37109) Full Text: DOI
Xu, Tao; Tian, Bo; Zhang, Hai-Qiang; Li, Juan Integrable decompositions for the \((2+1)\)-dimensional Gardner equation. (English) Zbl 1192.35144 Z. Angew. Math. Phys. 61, No. 2, 293-308 (2010). MSC: 35Q51 37K10 37K35 35-04 35C08 PDFBibTeX XMLCite \textit{T. Xu} et al., Z. Angew. Math. Phys. 61, No. 2, 293--308 (2010; Zbl 1192.35144) Full Text: DOI
Cai, Ke-Jie; Tian, Bo; Zhang, Huan; Meng, Xiang-Hua Direct approach to construct the periodic wave solutions for two nonlinear evolution equations. (English) Zbl 1183.37108 Commun. Theor. Phys. 52, No. 3, 473-478 (2009). MSC: 37K10 37K40 37B10 14A25 35Q53 35Q51 PDFBibTeX XMLCite \textit{K.-J. Cai} et al., Commun. Theor. Phys. 52, No. 3, 473--478 (2009; Zbl 1183.37108) Full Text: DOI
Lü, Xing; Geng, Tao; Zhang, Cheng; Zhu, Hong-Wu; Meng, Xiang-Hua; Tian, Bo Multi-soliton solutions and their interactions for the \((2+1)\)-dimensional Sawada-Kotera model with truncated Painlevé expansion, Hirota bilinear method and symbolic computation. (English) Zbl 1180.37094 Int. J. Mod. Phys. B 23, No. 25, 5003-5015 (2009). MSC: 37K10 34M55 35Q53 68W30 PDFBibTeX XMLCite \textit{X. Lü} et al., Int. J. Mod. Phys. B 23, No. 25, 5003--5015 (2009; Zbl 1180.37094) Full Text: DOI
Li, Hong-Zhe; Tian, Bo; Lü, Xing; Zhang, Hai-Qiang The Darboux transformation and soliton solutions for a new \((2+1)\)-dimensional variant Boussinesq system in shallow water with symbolic computation. (English) Zbl 1179.35274 Phys. Scr. 80, No. 3, Article ID 035002 (2009). MSC: 35Q51 35Q35 35C08 37K10 35A30 37K35 PDFBibTeX XMLCite \textit{H.-Z. Li} et al., Phys. Scr. 80, No. 3, Article ID 035002 (2009; Zbl 1179.35274) Full Text: DOI
Meng, Xiang-Hua; Tian, Bo; Feng, Qian; Yao, Zhen-Zhi; Ga, Yi-Tian Painlevé analysis and determinant solutions of a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in wronskian and grammian form. (English) Zbl 1187.37101 Commun. Theor. Phys. 51, No. 6, 1062-1068 (2009). Reviewer: Galina Filipuk (Warszawa) MSC: 37K10 PDFBibTeX XMLCite \textit{X.-H. Meng} et al., Commun. Theor. Phys. 51, No. 6, 1062--1068 (2009; Zbl 1187.37101) Full Text: DOI
Zhang, Hai-Qiang; Tian, Bo; Li, Juan; Xu, Tao; Zhang, Ya-Xing Symbolic-computation study of integrable properties for the \((2+1)\)-dimensional Gardner equation with the two-singular manifold method. (English) Zbl 1168.35439 IMA J. Appl. Math. 74, No. 1, 46-61 (2009). MSC: 35Q58 35A30 37K10 37K35 PDFBibTeX XMLCite \textit{H.-Q. Zhang} et al., IMA J. Appl. Math. 74, No. 1, 46--61 (2009; Zbl 1168.35439) Full Text: DOI arXiv
Yang, Zai-Chun; Tian, Bo Remarks on the Painlevé analysis for a \((2+1)\)-dimensional generalization of nonlinear Schrödinger-type equations. (English) Zbl 1144.81428 J. Math. Phys. 48, No. 7, 073508, 3 p. (2007). MSC: 35Q55 37K10 PDFBibTeX XMLCite \textit{Z.-C. Yang} and \textit{B. Tian}, J. Math. Phys. 48, No. 7, 073508, 3 p. (2007; Zbl 1144.81428) Full Text: DOI
Tian, Bo; Wei, Guang-Mei; Zhang, Chun-Yi; Shan, Wen-Rui; Gao, Yi-Tian Transformations for a generalized variable-coefficient Korteweg-de Vries model from blood vessels, Bose-Einstein condensates, rods and positons with symbolic computation. (English) Zbl 1160.37401 Phys. Lett., A 356, No. 1, 8-16 (2006). MSC: 37K10 92C35 82D99 68W30 PDFBibTeX XMLCite \textit{B. Tian} et al., Phys. Lett., A 356, No. 1, 8--16 (2006; Zbl 1160.37401) Full Text: DOI
Tian, Bo Similarity reductions for a generalized variable-coefficient Kadomtsev-Petviashvili equation with symbolic computation. (English) Zbl 0945.37021 Int. J. Mod. Phys. C 10, No. 6, 1089-1097 (1999). MSC: 37K10 35Q53 37-04 37K20 PDFBibTeX XMLCite \textit{B. Tian}, Int. J. Mod. Phys. C 10, No. 6, 1089--1097 (1999; Zbl 0945.37021) Full Text: DOI
Tian, Bo; Gao, Yi-Tian Analytical solving of a deformed KdV equation. (English) Zbl 0947.37036 Czech. J. Phys. 47, No. 6, 603-606 (1997). MSC: 37K10 35C99 35Q53 PDFBibTeX XMLCite \textit{B. Tian} and \textit{Y.-T. Gao}, Czech. J. Phys. 47, No. 6, 603--606 (1997; Zbl 0947.37036) Full Text: DOI
Tian, Bo; Gao, Yi-Tian Soliton-like solutions to the \((2+1)\)-dimensional integrable dispersive long wave equations. (English) Zbl 1063.37572 Phys. Scr. 53, No. 6, 641-642 (1996). MSC: 37K40 37K35 37K10 35Q51 PDFBibTeX XMLCite \textit{B. Tian} and \textit{Y.-T. Gao}, Phys. Scr. 53, No. 6, 641--642 (1996; Zbl 1063.37572) Full Text: DOI Link