Liu, Xing-yu; Lu, Bin-he; Zhang, Da-jun New type of solutions for the modified Korteweg-de Vries equation. (English) Zbl 07927832 Appl. Math. Lett. 159, Article ID 109288, 5 p. (2025). Reviewer: Guido Schneider (Stuttgart) MSC: 37K40 37K10 35Q53 35C08 35C09 × Cite Format Result Cite Review PDF Full Text: DOI
Liang, Zu-feng; Tang, Xiao-yan; Ding, Wei High-dimensional nonlinear variable separation solutions and novel wave excitations for the \((4 + 1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. (English) Zbl 07955074 Commun. Theor. Phys. 76, No. 11, Article ID 115001, 11 p. (2024). MSC: 37K10 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Xing; Zhang, Da-Jun The Lamé functions and elliptic soliton solutions: bilinear approach. (English) Zbl 07954887 Filipuk, Galina (ed.), Recent progress in special functions. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 807, 171-195 (2024). MSC: 33E10 33E05 33E30 37K20 37K10 35C08 35Q51 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lan, Zhong-Zhou \(N\)-soliton solutions, Bäcklund transformation and Lax pair for a generalized variable-coefficient cylindrical Kadomtsev-Petviashvili equation. (English) Zbl 1546.35154 Appl. Math. Lett. 158, Article ID 109239, 6 p. (2024). MSC: 35Q35 35Q53 35C08 37K35 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Hao, Xiazhi; Lou, S. Y. Decomposition solutions and Bäcklund transformations of the B-type and C-type Kadomtsev-Petviashvili equations. (English) Zbl 1544.35134 Commun. Theor. Phys. 76, No. 6, Article ID 065004, 11 p. (2024). MSC: 35Q51 37K10 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Jing; Zhang, Da-jun; Maruno, Ken-ichi Connection between the symmetric discrete AKP system and bilinear ABS lattice equations. (English) Zbl 1547.37094 Physica D 462, Article ID 134155, 18 p. (2024). MSC: 37K60 39A36 39A14 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Yu-Lan; Li, Bang-Qing The dynamics on soliton molecules and soliton bifurcation for an extended generalization of Vakhnenko equation. (English) Zbl 07840585 Qual. Theory Dyn. Syst. 23, No. 3, Paper No. 137, 13 p. (2024). MSC: 78-XX × Cite Format Result Cite Review PDF Full Text: DOI
Guo, Ming-Juan; Wen, Xiao-Yong; Liu, Xue-Ke Various types of discrete exact localized wave solutions and dynamical analysis for the discrete complex modified Korteweg-de Vries equation. (English) Zbl 07825049 Wave Motion 125, Article ID 103260, 16 p. (2024). MSC: 35-XX 37-XX × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Da-Jun; Liu, Shi-Min; Deng, Xiao The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: bilinearisation and reduction approach. (English) Zbl 1545.35187 Open Commun. Nonlinear Math. Phys. 3, 23-66 (2023). MSC: 35Q55 35Q41 35C08 35C05 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Silem, Abdselam; Lin, Ji; Akhtar, Naeem Nonautonomous dynamics of local and nonlocal Fokas-Lenells models. (English) Zbl 1522.35145 J. Phys. A, Math. Theor. 56, No. 36, Article ID 365201, 19 p. (2023). MSC: 35C08 35G55 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Yu-Lan; Li, Bang-Qing Interaction behaviors between solitons, breathers and their hybrid forms for a short pulse equation. (English) Zbl 1522.35143 Qual. Theory Dyn. Syst. 22, No. 4, Paper No. 146, 17 p. (2023). MSC: 35C08 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Zong-Ao; Lou, Sen-Yue Some special exact solutions in nonlocal Alice-Bob sine-Gordon systems. (English) Zbl 1516.35365 Commun. Theor. Phys. 75, No. 2, Article ID 025004, 7 p. (2023). MSC: 35Q51 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Yu-Qi; Tian, Bo; Wei, Cheng-Cheng; Yang, Dan-Yu Bilinear forms and solitonic stability for a variable-coefficient Hirota-Satsuma coupled Korteweg-de Vries system in a liquid. (English) Zbl 1523.35113 Phys. Lett., A 477, Article ID 128865, 9 p. (2023). MSC: 35C08 35Q51 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Silem, Abdselam; Lin, Ji Exact solutions for a variable-coefficients nonisospectral nonlinear Schrödinger equation via Wronskian technique. (English) Zbl 1501.35378 Appl. Math. Lett. 135, Article ID 108397, 9 p. (2023). MSC: 35Q55 35Q41 35C08 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Shu-zhi; Wang, Jing; Zhang, Da-jun The Fokas-Lenells equations: bilinear approach. (English) Zbl 1529.35474 Stud. Appl. Math. 148, No. 2, 651-688 (2022). MSC: 35Q55 35Q41 35Q40 35Q15 35P25 35C08 35B40 78A60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Hongcai; Gao, Yidan; Deng, Aiping Dynamical analysis of diversity lump solutions to the \((2+1)\)-dimensional dissipative Ablowitz-Kaup-Newell-Segure equation. (English) Zbl 1516.35359 Commun. Theor. Phys. 74, No. 11, Article ID 115003, 10 p. (2022). MSC: 35Q51 35C08 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Xing; Zhang, Da-jun Elliptic soliton solutions: \(\tau\) functions, vertex operators and bilinear identities. (English) Zbl 1503.37075 J. Nonlinear Sci. 32, No. 5, Paper No. 70, 53 p. (2022). MSC: 37K10 37K40 37K20 35Q51 35C07 35C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Shi-min; Wang, Jing; Zhang, Da-jun Solutions to integrable space-time shifted nonlocal equations. (English) Zbl 1535.35164 Rep. Math. Phys. 89, No. 2, 199-220 (2022). MSC: 35Q53 37K35 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Wen-Xiu \(N\)-soliton solutions and the Hirota conditions in (1 + 1)-dimensions. (English) Zbl 07533159 Int. J. Nonlinear Sci. Numer. Simul. 23, No. 1, 123-133 (2022). MSC: 35Q51 35Q53 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Yong; Wei, Juncheng Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane. (English) Zbl 1486.35196 Rev. Mat. Iberoam. 38, No. 2, 355-432 (2022). MSC: 35J61 35B08 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Yujuan; Ma, Ruyun; Xiong, Na; Feng, Bao-Feng Integrable semi-discretization of a modified short wave equation. (English) Zbl 1485.37067 Appl. Math. Lett. 125, Article ID 107739, 8 p. (2022). MSC: 37K60 37K10 37K35 37K40 39A36 39A14 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Jing; Wu, Hua On \((2+1)\)-dimensional mixed AKNS hierarchy. (English) Zbl 1477.35229 Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 106052, 13 p. (2022). MSC: 35Q53 37K10 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Silem, Abdselam; Wu, Hua; Zhang, Da-jun Nonisospectral effects on generating localized waves. (English) Zbl 1514.35096 Commun. Theor. Phys. 73, No. 11, Article ID 115002, 13 p. (2021). MSC: 35C08 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Akbar, Yasir; Afsar, Haleem; Al-Mubaddel, Fahad S.; Abu-Hamdeh, Nidal H.; Abusorrah, Abdullah M. On the solitary wave solution of the viscosity capillarity van der Waals \(p\)-system along with Painleve analysis. (English) Zbl 1498.35150 Chaos Solitons Fractals 153, Part 1, Article ID 111495, 12 p. (2021). MSC: 35C08 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI
Chai, Xuedong; Zhang, Yufeng; Zhao, Shiyin Application of the \(\bar\partial \)-dressing method to a \((2+1)\)-dimensional equation. (English. Russian original) Zbl 1486.81147 Theor. Math. Phys. 209, No. 3, 1717-1725 (2021); translation from Teor. Mat. Fiz. 209, No. 3, 465-474 (2021). MSC: 81T10 81T15 35J08 35R30 81U40 35C08 35G31 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Haifeng; Zhang, Yufeng \( \bar\partial \)-dressing method for a few \((2+1)\)-dimensional integrable coupling systems. (English. Russian original) Zbl 1482.81040 Theor. Math. Phys. 208, No. 3, 1239-1255 (2021); translation from Teor. Mat. Fiz. 208, No. 3, 452-470 (2021). MSC: 81U40 81U15 81Q80 81T10 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu \(N\)-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation. (English) Zbl 1540.35103 Math. Comput. Simul. 190, 270-279 (2021). MSC: 35C08 35Q53 35Q51 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Cho, Aye Aye; Mesfun, Maebel; Zhang, Da-Jun A revisit to the ABS H2 equation. (English) Zbl 1477.35216 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 093, 19 p. (2021). MSC: 35Q53 37K60 37K10 37K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Wen-Xiu; Yong, Xuelin; Lü, Xing Soliton solutions to the B-type Kadomtsev-Petviashvili equation under general dispersion relations. (English) Zbl 1524.35508 Wave Motion 103, Article ID 102719, 7 p. (2021). MSC: 35Q51 35Q53 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Jia, Yuechen; Lu, Yu; Yu, Miao; Gegen, Hasi \(M\)-breather, lumps, and soliton molecules for the \((2 + 1)\)-dimensional elliptic Toda equation. (English) Zbl 1479.35407 Adv. Math. Phys. 2021, Article ID 5211451, 18 p. (2021). MSC: 35J61 35A01 × Cite Format Result Cite Review PDF Full Text: DOI
Duarte, V. N. A class of solutions of the two-dimensional Toda lattice equation. (English) Zbl 1487.37083 Phys. Lett., A 385, Article ID 126979, 3 p. (2021). Reviewer: Andrei Pranevich (Grodno) MSC: 37K10 35C08 37K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Wen-Xiu \(N\)-soliton solution of a combined pKP-BKP equation. (English) Zbl 1470.35310 J. Geom. Phys. 165, Article ID 104191, 7 p. (2021). MSC: 35Q53 35Q51 37K40 37K10 35C06 × Cite Format Result Cite Review PDF Full Text: DOI
Silem, Abdselam; Wu, Hua; Zhang, Da-jun Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schrödinger equation. (English) Zbl 1462.39004 Appl. Math. Lett. 116, Article ID 107049, 8 p. (2021). MSC: 39A12 39A36 39A14 35Q55 35B44 35C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Bang-Qing Loop-like kink breather and its transition phenomena for the Vakhnenko equation arising from high-frequency wave propagation in electromagnetic physics. (English) Zbl 1453.78003 Appl. Math. Lett. 112, Article ID 106822, 8 p. (2021). MSC: 78A40 78A60 35Q51 35Q55 35C08 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Bang-Qing; Ma, Yu-Lan Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation. (English) Zbl 1517.35087 Nonlinear Dyn. 102, No. 3, 1787-1799 (2020). MSC: 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Two new Painlevé-integrable (2+1) and (3+1)-dimensional KdV equations with constant and time-dependent coefficients. (English) Zbl 1479.35752 Nucl. Phys., B 954, Article ID 115009, 10 p. (2020). MSC: 35Q53 35Q51 35C08 37K10 35A25 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Lan; Zhou, Yuqian; Liu, Qian; Zhang, Qiuyan Traveling waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation. (English) Zbl 1464.37075 J. Appl. Anal. Comput. 10, No. 1, 267-281 (2020). MSC: 37K50 35B32 35C07 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Shimin; Hua, Wu; Zhang, Da-Jun New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential. (English) Zbl 1527.35323 Rep. Math. Phys. 86, No. 3, 271-292 (2020). MSC: 35Q40 81Q80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Ning; Xu, Xi-Xiang Positive and negative integrable hierarchies: bi-Hamiltonian structure and Darboux-Bäcklund transformation. (English) Zbl 1459.37057 Math. Probl. Eng. 2020, Article ID 5363952, 15 p. (2020). MSC: 37K10 35Q53 37K60 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Jing; Wu, Hua; Zhang, Da-jun Solutions of the nonlocal \((2+1)\)-D breaking solitons hierarchy and the negative order AKNS hierarchy. (English) Zbl 1451.35054 Commun. Theor. Phys. 72, No. 4, Article ID 045002, 12 p. (2020). MSC: 35C08 35Q51 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Guan, Xue; Zhou, Qin; Biswas, Anjan; Kamis Alzahrani, Abdullah; Liu, Wenjun Darboux transformation for a generalized Ablowitz-Kaup-Newell-Segur hierarchy equation. (English) Zbl 1448.37078 Phys. Lett., A 384, No. 18, Article ID 126394, 6 p. (2020). MSC: 37K10 37J35 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Cui, Chao-jie; Tang, Xiao-yan; Cui, Ya-jun New variable separation solutions and wave interactions for the \((3+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. (English) Zbl 1443.37052 Appl. Math. Lett. 102, Article ID 106109, 6 p. (2020). MSC: 37K35 37K40 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Xiaorui; Lin, Shuning; Shen, Shoufeng New interaction solutions to (1+1)-dimensional Ito equation. (English) Zbl 1428.35096 Appl. Math. Lett. 101, Article ID 106071, 7 p. (2020). MSC: 35G25 35C08 68W30 35C05 × Cite Format Result Cite Review PDF Full Text: DOI
Hayashi, Masahito; Shigemoto, Kazuyasu; Tsukioka, Takuya The construction of the mKdV cyclic symmetric \(N\)-soliton solution by the Bäcklund transformation. (English) Zbl 1416.35230 Mod. Phys. Lett. A 34, No. 18, Article ID 1950136, 16 p. (2019). MSC: 35Q53 35C08 35A22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Deng, Xiao; Lou, Senyue; Zhang, Dajun Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrödinger equations. (English) Zbl 1427.35252 Appl. Math. Comput. 332, 477-483 (2018). MSC: 35Q55 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Chuanjian; Fang, Hui Bilinear Bäcklund transformations, kink periodic solitary wave and lump wave solutions of the Bogoyavlenskii-Kadomtsev-Petviashvili equation. (English) Zbl 1420.35329 Comput. Math. Appl. 76, No. 1, 1-10 (2018). MSC: 35Q53 35A30 37K40 35C07 35C08 35B10 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Xi-Xiang; Xu, Meng A family of integrable different-difference equations, its Hamiltonian structure, and Darboux-Bäcklund transformation. (English) Zbl 1417.39062 Discrete Dyn. Nat. Soc. 2018, Article ID 4152917, 11 p. (2018). MSC: 39A30 × Cite Format Result Cite Review PDF Full Text: DOI
Zarmi, Yair Soliton-generating \(\tau\)-functions revisited. (English) Zbl 1406.35323 J. Math. Phys. 59, No. 12, 122701, 21 p. (2018). MSC: 35Q51 35Q53 37K40 35C08 37K15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhu, Junyi; Wang, Linlin; Geng, Xianguo Riemann-Hilbert approach to TD equation with nonzero boundary condition. (English) Zbl 1402.35195 Front. Math. China 13, No. 5, 1245-1265 (2018). MSC: 35P25 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Kui; Deng, Xiao; Lou, Senyue; Zhang, Da-jun Solutions of nonlocal equations reduced from the AKNS hierarchy. (English) Zbl 1398.35194 Stud. Appl. Math. 141, No. 1, 113-141 (2018). MSC: 35Q53 35Q55 35C08 35B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Yi; Xu, Yin-Kang; Shi, Yu-Bin Rational solutions for a combined \((3+1)\)-dimensional generalized BKP equation. (English) Zbl 1390.35290 Nonlinear Dyn. 91, No. 2, 1337-1347 (2018). MSC: 35Q35 37K10 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Sun, Jianqing; Hu, Xingbiao; Zhang, Yingnan A semi-discrete modified KdV equation. (English) Zbl 1393.35209 J. Math. Phys. 59, No. 4, 043505, 12 p. (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 39A14 35C08 37K10 37K60 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Kui; Zhang, Da-jun Solutions of the nonlocal nonlinear Schrödinger hierarchy via reduction. (English) Zbl 1379.35289 Appl. Math. Lett. 75, 82-88 (2018). MSC: 35Q55 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing Solitons, Bäcklund transformation and Lax pair for a \((2+1)\)-dimensional Broer-Kaup-Kupershmidt system in the shallow water of uniform depth. (English) Zbl 1465.37080 Commun. Nonlinear Sci. Numer. Simul. 44, 360-372 (2017). MSC: 37K40 37K35 35C08 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Zhao, Hai-qiong; Ma, Wen-Xiu Mixed lump-kink solutions to the KP equation. (English) Zbl 1394.35461 Comput. Math. Appl. 74, No. 6, 1399-1405 (2017). MSC: 35Q53 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Yu, Jian-Ping; Sun, Yong-Li A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation. (English) Zbl 1393.37087 Nonlinear Dyn. 90, No. 4, 2263-2268 (2017). MSC: 37K35 35C07 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Bang-Qing; Ma, Yu-Lan; Mo, Li-Po; Fu, Ying-Ying The \(N\)-loop soliton solutions for \((2+1)\)-dimensional Vakhnenko equation. (English) Zbl 1387.35520 Comput. Math. Appl. 74, No. 3, 504-512 (2017). MSC: 35Q51 35C08 35Q83 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Lan, Zhong-Zhou; Gao, Yi-Tian; Zhao, Chen; Yang, Jin-Wei; Su, Chuan-Qi Solitons, Bäcklund transformation and Lax pair for a variable-coefficient generalized Boussinesq system in the shallow water. (English) Zbl 1366.37136 Waves Random Complex Media 27, No. 2, 255-264 (2017). MSC: 37K40 37K10 76B15 35C08 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Deng, Shufang Bell polynomials to the Kadomtsev-Petviashivili equation with self-consistent sources. (English) Zbl 1488.35479 Adv. Appl. Math. Mech. 8, No. 2, 271-278 (2016). MSC: 35Q53 35A30 × Cite Format Result Cite Review PDF Full Text: DOI
Singh, Manjit; Gupta, R. K. Bäcklund transformations, Lax system, conservation laws and multisoliton solutions for Jimbo-Miwa equation with Bell-polynomials. (English) Zbl 1473.35492 Commun. Nonlinear Sci. Numer. Simul. 37, 362-373 (2016). MSC: 35Q53 35A30 35C08 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Zhigang; Tao, Xiuli Bilinear Bäcklund transformations and explicit solutions of a \((3+1)\)-dimensional nonlinear equation. (English) Zbl 1419.37068 Adv. Difference Equ. 2016, Paper No. 312, 13 p. (2016). MSC: 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Vakhnenko, V. O.; Parkes, E. J. Approach in theory of nonlinear evolution equations: the Vakhnenko-Parkes equation. (English) Zbl 1455.35217 Adv. Math. Phys. 2016, Article ID 2916582, 39 p. (2016). Reviewer: Solomon Manukure (Austin) MSC: 35Q51 37K15 35C08 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Integrable couplings of the generalized Vakhnenko equation: multiple soliton solutions. (English) Zbl 1358.35162 J. Vib. Control 22, No. 4, 915-919 (2016). MSC: 35Q53 35Q60 35Q74 35C05 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Li, He; Gao, Yi-Tian Bilinear form and two Bäcklund transformations for the \((3+1)\)-dimensional Jimbo-Miwa equation. (English) Zbl 1433.35342 Abstr. Appl. Anal. 2015, Article ID 834521, 5 p. (2015). MSC: 35Q53 35A30 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Krishnakumar, K.; Tamizhmani, K. M.; Leach, P. G. L. Algebraic solutions of the Hirota bilinear form for the Korteweg-de Vries and Boussinesq equations. (English) Zbl 1352.35147 Indian J. Pure Appl. Math. 46, No. 5, 739-756 (2015). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35Q53 35Q35 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, YingNan; Chang, XiangKe; Hu, Juan; Hu, XingBiao; Tam, Hon-Wah Integrable discretization of soliton equations via bilinear method and Bäcklund transformation. (English) Zbl 1309.37065 Sci. China, Math. 58, No. 2, 279-296 (2015). MSC: 37K10 37J35 37K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Na; Ding, Feng Lax pair, Bäcklund transformation and conservation laws for the \((2 + 1)\)-dimensional extended shallow water wave equation. (English) Zbl 1391.76072 Comput. Fluids 89, 153-156 (2014). MSC: 76B15 76M60 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Two B-type Kadomtsev-Petviashvili equations of \((2+1)\) and \((3+1)\) dimensions: multiple soliton solutions, rational solutions and periodic solutions. (English) Zbl 1290.35028 Comput. Fluids 86, 357-362 (2013). MSC: 35C05 35C08 35Q53 35B10 76M25 76B25 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Couplings of a fifth order nonlinear integrable equation: multiple kink solutions. (English) Zbl 1290.35233 Comput. Fluids 84, 97-99 (2013). MSC: 35Q53 37K10 35A30 76B25 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu Bilinear equations and resonant solutions characterized by Bell polynomials. (English) Zbl 1396.35054 Rep. Math. Phys. 72, No. 1, 41-56 (2013). MSC: 35Q53 35A30 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu Trilinear equations, Bell polynomials, and resonant solutions. (English) Zbl 1276.35131 Front. Math. China 8, No. 5, 1139-1156 (2013). MSC: 35Q51 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid A variety of distinct kinds of multiple soliton solutions for a \((3+1)\)-dimensional nonlinear evolution equation. (English) Zbl 1510.35112 Math. Methods Appl. Sci. 36, No. 3, 349-357 (2013). MSC: 35C08 35B25 35Q51 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu; Zhu, Zuonong Solving the \((3+1)\)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. (English) Zbl 1280.35122 Appl. Math. Comput. 218, No. 24, 11871-11879 (2012). MSC: 35Q51 35Q53 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Li, He; Meng, Xiang-Hua; Tian, Bo Bilinear form and soliton solutions for the coupled nonlinear Klein-Gordon equations. (English) Zbl 1260.35206 Int. J. Mod. Phys. B 26, No. 15, Article ID 1250057, 10 p. (2012). MSC: 35Q55 35C08 33E17 × Cite Format Result Cite Review PDF Full Text: DOI
Conde, Juan M.; Gordoa, Pilar R.; Pickering, Andrew A new kind of Bäcklund transformation for partial differential equations. (English) Zbl 1386.37071 Rep. Math. Phys. 70, No. 2, 149-161 (2012). Reviewer: Ivan C. Sterling (St. Mary’s City) MSC: 37K35 35A30 37K05 × Cite Format Result Cite Review PDF Full Text: DOI
Abdeljabbar, Alrazi; Ma, Wenxiu; Yildirim, Ahmet Determinant solutions to a \((3+1)\)-dimensional generalized KP equation with variable coefficients. (English) Zbl 1263.65100 Chin. Ann. Math., Ser. B 33, No. 5, 641-650 (2012). Reviewer: Petr Sváček (Praha) MSC: 65M99 35Q53 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu; Abdeljabbar, Alrazi A bilinear Bäcklund transformation of a \((3+1)\)-dimensional generalized KP equation. (English) Zbl 1248.37070 Appl. Math. Lett. 25, No. 10, 1500-1504 (2012). MSC: 37K35 37K10 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid A study on the \((2 + 1)\)-dimensional and the \((2 + 1)\)-dimensional higher-order Burgers equations. (English) Zbl 1252.35233 Appl. Math. Lett. 25, No. 10, 1495-1499 (2012). MSC: 35Q35 35A22 × Cite Format Result Cite Review PDF Full Text: DOI
Qu, Qi-Xing; Tian, Bo; Liu, Wen-Jun; Wang, Pan; Jiang, Yan Soliton solutions and Bäcklund transformation for the normalized linearly coupled nonlinear wave equations with symbolic computation. (English) Zbl 1248.35177 Appl. Math. Comput. 218, No. 21, 10386-10392 (2012). MSC: 35Q51 35C08 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Do, Younghae; Jang, Bongsoo Nonlinear Klein-Gordon and Schrödinger equations by the projected differential transform method. (English) Zbl 1246.65235 Abstr. Appl. Anal. 2012, Article ID 150527, 15 p. (2012). MSC: 65N99 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI
Lü, Xing; Tian, Bo; Zhang, Hai-Qiang; Xu, Tao; Li, He Generalized (2 + 1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms. (English) Zbl 1247.35107 Nonlinear Dyn. 67, No. 3, 2279-2290 (2012). MSC: 35Q35 35Q86 35A22 76L05 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu; Zhang, Yi; Tang, Yaning; Tu, Junyi Hirota bilinear equations with linear subspaces of solutions. (English) Zbl 1245.35109 Appl. Math. Comput. 218, No. 13, 7174-7183 (2012). MSC: 35Q53 11D09 35C07 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Multiple-soliton solutions for a \((3 + 1)\)-dimensional generalized KP equation. (English) Zbl 1245.35104 Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 491-495 (2012). MSC: 35Q51 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Huang, Lin; Zhang, Da-Jun Solutions and Lax pairs based on bilinear Bäcklund transformations of some supersymmetric equations. (English) Zbl 1238.35003 J. Nonlinear Math. Phys. 19, No. 1, 1250005, 14 p. (2012). MSC: 35A22 35Q53 58J72 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Jun-Min; Yang, Xiao Quasi-periodic wave solutions for the \((2+1)\)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (CBS) equation. (English) Zbl 1242.35027 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2256-2261 (2012). MSC: 35B15 35A22 35Q51 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu Combined Wronskian solutions to the 2D Toda molecule equation. (English) Zbl 1254.37045 Phys. Lett., A 375, No. 45, 3931-3935 (2011). MSC: 37K10 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Jian-Bing; Zhang, Da-Jun; Shen, Qing Bilinear approach for a symmetry constraint of the modified KdV equation. (English) Zbl 1244.35132 Appl. Math. Comput. 218, No. 8, 4494-4500 (2011). MSC: 35Q53 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Pan; Tian, Bo; Liu, Wen-Jun; Lü, Xing; Jiang, Yan Lax pair, Bäcklund transformation and multi-soliton solutions for the Boussinesq-Burgers equations from shallow water waves. (English) Zbl 1433.35302 Appl. Math. Comput. 218, No. 5, 1726-1734 (2011). MSC: 35Q35 35C08 37K35 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Multiple soliton solutions for (2 + 1)-dimensional Sawada-Kotera and Caudrey-Dodd-Gibbon equations. (English) Zbl 1219.35215 Math. Methods Appl. Sci. 34, No. 13, 1580-1586 (2011). MSC: 35Q51 35Q53 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Wen-Xiu; Abdeljabbar, Alrazi; Asaad, Magdy Gamil Wronskian and Grammian solutions to a \((3 + 1)\)-dimensional generalized KP equation. (English) Zbl 1225.65098 Appl. Math. Comput. 217, No. 24, 10016-10023 (2011). Reviewer: Nicolae Pop (Baia Mare) MSC: 65M70 37K10 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Hongwei; Yin, Baoshu; Dong, Huanhe Frobenius integrable decompositions for high-order nonlinear evolution equations. (English) Zbl 1218.35195 Commun. Nonlinear Sci. Numer. Simul. 16, No. 8, 3005-3010 (2011). MSC: 35Q51 35A30 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Yi; Dang, Xiao-lan; Xu, Hong-xian Bäcklund transformations and soliton solutions for the KdV6 equation. (English) Zbl 1214.37048 Appl. Math. Comput. 217, No. 13, 6230-6236 (2011). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37K35 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Burgers hierarchy: multiple kink solutions and multiple singular kink solutions. (English) Zbl 1298.35167 J. Franklin Inst. 347, No. 3, 618-626 (2010). MSC: 35Q51 37K40 × Cite Format Result Cite Review PDF Full Text: DOI
Parkes, E. J. A note on loop-soliton solutions of the short-pulse equation. (English) Zbl 1238.35119 Phys. Lett., A 374, No. 42, 4321-4323 (2010). MSC: 35Q51 35C08 × Cite Format Result Cite Review PDF Full Text: DOI
Nandy, Sudipta; Sarma, Debojit; Barthakur, Abhijit; Borah, Abhijit Hirota bilinearization of coupled higher-order nonlinear Schrödinger equation. (English) Zbl 1222.35190 Commun. Nonlinear Sci. Numer. Simul. 15, No. 11, 3386-3389 (2010). MSC: 35Q55 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Multiple-soliton solutions of the perturbed KdV equation. (English) Zbl 1222.65134 Commun. Nonlinear Sci. Numer. Simul. 15, No. 11, 3270-3273 (2010). MSC: 65N99 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid A study on an integrable system of coupled KdV equations. (English) Zbl 1222.37070 Commun. Nonlinear Sci. Numer. Simul. 15, No. 10, 2846-2850 (2010). MSC: 37K10 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Completely integrable coupled KdV and coupled KP systems. (English) Zbl 1222.37069 Commun. Nonlinear Sci. Numer. Simul. 15, No. 10, 2828-2835 (2010). MSC: 37K10 35Q40 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Multiple soliton solutions for a \((2 + 1)\)-dimensional integrable KdV6 equation. (English) Zbl 1221.35371 Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1466-1472 (2010). MSC: 35Q53 37K20 × Cite Format Result Cite Review PDF Full Text: DOI
Wazwaz, Abdul-Majid Burgers hierarchy in \((2+1)\)-dimensions: multiple kink solutions and multiple singular kink solutions. (English) Zbl 1225.35191 Int. J. Nonlinear Sci. 10, No. 1, 3-11 (2010). MSC: 35Q51 35A22 37K10 × Cite Format Result Cite Review PDF