Soliton, breather, lump and their interaction solutions of the (2+1)-dimensional asymmetrical Nizhnik\u2013Novikov\u2013Veselov equation

Yaqing Liu,Xiao-Yong Wen

doi:10.1186/s13662-019-2271-5

Yaqing Liu, Xiao-Yong Wen

Open Access

https://doi.org/10.1186/s13662-019-2271-5

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Abstract

In this work, the (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation is investigated. Hirota’s bilinear method is used to determine the N-soliton solutions for this equation, from which the M-lump solutions are obtained by using long wave limit when N is even (i.e., N=2M). Then, taking N=5 as an example, we discuss some novel mixed lump-soliton and lump-soliton-breather solutions by using long wave limit and choosing special conjugate complex parameters from the five-soliton solution. Figures are plotted to reveal the dynamical features of such obtained lump and mixed interaction solutions. These results may be useful for understanding the propagation phenomena of nonlinear localized waves.

Highlights

Nonlinear evolution equations are well used to describe various significant nonlinear phenomena in nature, which display significant prosperities as the soliton solution, infinite number of conservation laws, symmetries, and Hamiltonian structures
A set of systematic methods have been used in the literature to obtain reliable treatments of nonlinear evolution equations
4 The lump interacts with soliton or breather In the previous section, we discussed the M-lump solutions of Eq (1) by use of long wave limit

Summary

Introduction

Nonlinear evolution equations are well used to describe various significant nonlinear phenomena in nature, which display significant prosperities as the soliton solution, infinite number of conservation laws, symmetries, and Hamiltonian structures. 4, we take odd five-soliton solution as an example and give some mixed lump-soliton and lump-solitonbreather solutions by using long wave limit and choosing special parameters.

Results

Conclusion