General lump-type solutions of the (3+1)-dimensional Jimbo-Miwa equation

Abstract In this paper, we study the general lump-type solutions of the (3+1)-dimensional Jimbo–Miwa equation via Hirota bilinear method and the ansatz technique. In contrast with lump solutions presented before, we firstly find a general quadratic function solution of the transformed bilinear Jimbo–Miwa equation and then expand it as the sums of squares of linear functions to satisfy analyticity condition. Especially, we get a lump-type solution with fifteen parameters which possess eleven arbitrary independent parameters and four constraint conditions. This solution supplements the existing lump-type solutions obtained previously in the literature. Finally, we conclude that there are only two linearly independent non-constant linear functions in the summation for a positive quadratic function solution.

[1]  Xiaoen Zhang,et al.  Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation , 2016, Commun. Nonlinear Sci. Numer. Simul..

[2]  Wen-Xiu Ma,et al.  Lump solutions to nonlinear partial differential equations via Hirota bilinear forms , 2016, 1607.06983.

[3]  Hong-Qian Sun,et al.  Lump and lump-kink solutions of the (3+1)-dimensional Jimbo-Miwa and two extended Jimbo-Miwa equations , 2017, Appl. Math. Lett..

[4]  S. Novikov,et al.  Theory of Solitons: The Inverse Scattering Method , 1984 .

[5]  Yi Zhang,et al.  Generalized Wronskian solutions for the (3 + 1)-dimensional Jimbo-Miwa equation , 2012, Appl. Math. Comput..

[6]  Huanhe Dong,et al.  Hybrid Solutions of (3 + 1)-Dimensional Jimbo-Miwa Equation , 2017 .

[7]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[8]  Zhengde Dai,et al.  Exact three-wave solutions for the (3+1)-dimensional Jimbo-Miwa equation , 2011, Comput. Math. Appl..

[9]  Jian-bing Zhang,et al.  Mixed lump-kink solutions to the BKP equation , 2017, Comput. Math. Appl..

[10]  Manjit Singh.  New exact solutions for (3+1)-dimensional Jimbo–Miwa equation , 2016 .

[11]  Jian-Ping Fang,et al.  New exact solutions for the (3 + 1)-dimensional Jimbo–Miwa system , 2009 .

[12]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[13]  Z. Dai,et al.  Emergence and Interaction of the Lump-Type Solution with the (3+1)-D Jimbo-Miwa Equation , 2017 .

[14]  Wenxiu Ma,et al.  A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation , 2009, 0903.5337.

[15]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for extended (3+1)-dimensional Jimbo-Miwa equations , 2017, Appl. Math. Lett..

[16]  Yun-Hu Wang,et al.  Integrability for the generalised variable-coefficient fifth-order Korteweg-de Vries equation with Bell polynomials , 2014, Appl. Math. Lett..

[17]  J. Y. Yang,et al.  Abundant lump-type solutions of the Jimbo-Miwa equation in (3+1)-dimensions , 2017, Comput. Math. Appl..

[18]  Guiqiong Xu,et al.  The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in (3 + 1)-dimensions , 2006 .

[19]  Jian-bing Zhang,et al.  Bilinear approach for a symmetry constraint of the modified KdV equation , 2011, Appl. Math. Comput..

[20]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations , 2008, Appl. Math. Comput..

[21]  Yaning Tang.  Pfaffian solutions and extended Pfaffian solutions to (3 + 1)-dimensional Jimbo–Miwa equation , 2013 .

[22]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .