Lump solution and integrability for the associated Hirota bilinear equation

This paper studies lump solution and integrability for the associated Hirota bilinear equation. The integrability in the sense of Lax pair and the bilinear Bäcklund transformations is presented by the binary Bell polynomial method. The lump solution is derived when the period of complexiton solution goes to infinite. Conversely, complexiton solution can also be derived from the lump solution. Complexiton solution is a superposition structure of lump solutions. The dynamics of the lump solution are investigated and exhibited mathematically and graphically. These results further supplement and enrich the theories for the associated Hirota bilinear equation. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in nonlinear science.

[1]  Adem Kilicman,et al.  Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations , 2014 .

[2]  Jiahua Jin,et al.  Multiple solutions of the Kirchhoff-type problem in RN , 2016 .

[3]  V. Awati,et al.  Multigrid method for the solution of EHL line contact with bio-based oils as lubricants , 2016 .

[4]  Wen-Xiu Ma,et al.  Complexiton solutions to the Korteweg–de Vries equation , 2002 .

[5]  Bo Tian,et al.  Bell-polynomial construction of Bäcklund transformations with auxiliary independent variable for some soliton equations with one Tau-function , 2012 .

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

[8]  Zhengde Dai,et al.  Exact periodic kink-wave and degenerative soliton solutions for potential Kadomtsev-Petviashvili equation , 2010 .

[9]  Z. Dai,et al.  Resonance and deflection of multi-soliton to the (2+1)-dimensional Kadomtsev–Petviashvili equation , 2014 .

[10]  Wenxiu Ma,et al.  Trilinear equations, Bell polynomials, and resonant solutions , 2013 .

[11]  Manjit Singh,et al.  Bäcklund transformations, Lax system, conservation laws and multisoliton solutions for Jimbo-Miwa equation with Bell-polynomials , 2016, Commun. Nonlinear Sci. Numer. Simul..

[12]  Wenxiu Ma,et al.  Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials , 2013 .

[13]  Devendra Kumar,et al.  A fractional model of Navier–Stokes equation arising in unsteady flow of a viscous fluid , 2015 .

[14]  Wenxiu Ma,et al.  Lump solutions to the Kadomtsev–Petviashvili equation , 2015 .

[15]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[16]  Kenji Imai,et al.  DROMION AND LUMP SOLUTIONS OF THE ISHIMORI-I EQUATION , 1997 .

[17]  Kwok Wing Chow,et al.  The superposition of algebraic solitons for the modified Korteweg-de Vries equation , 2014, Commun. Nonlinear Sci. Numer. Simul..

[18]  Dumitru Baleanu,et al.  Numerical Computation of a Fractional Model of Differential-Difference Equation , 2016 .

[19]  Zhenyun Qin,et al.  Lump solutions to dimensionally reduced $$\varvec{p}$$p-gKP and $$\varvec{p}$$p-gBKP equations , 2016 .

[20]  Devendra Kumar,et al.  A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow , 2016, Entropy.

[21]  Wen-Xiu Ma,et al.  Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation , 2016 .

[22]  Wenxiu Ma,et al.  Complexiton solutions to integrable equations , 2005, nlin/0502035.

[23]  Wen-Xiu Ma,et al.  Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm , 2012, Appl. Math. Comput..