Various breathers and rogue waves for the coupled long-wave-short-wave system

Chuanjian Wang,Zhengde Dai

doi:10.1186/1687-1847-2014-87

Abstract

Explicit forms of various breathers, including inclined periodic breather, Akhmediev breather, Ma breather and rogue wave solutions, are obtained for the coupled long-wave-short-wave system by using a Hirota two-soliton method with complex frequency and complex wave number. Based on the structures of these breather solutions and figures via computer simulation, the characteristics of various breather solutions are discussed which might provide us with useful information on the dynamics of the relevant physical fields.

Highlights

It is well known that solitary wave solutions of nonlinear evolution equations play an important role in nonlinear science fields, especially in nonlinear physical science, since they can provide much physical information and more insight into the physical aspects of the problem and lead to further applications [ ]
We report the explicit forms of these breather solutions
3 Conclusion and discussion In this paper, the Hirota two-soliton method has been applied to the coupled long-waveshort-wave system

Summary

Introduction

It is well known that solitary wave solutions of nonlinear evolution equations play an important role in nonlinear science fields, especially in nonlinear physical science, since they can provide much physical information and more insight into the physical aspects of the problem and lead to further applications [ ]. The first-order rational solution of the self-focusing nonlinear Schödinger equation (NLS) was first found by Peregrine to describe the rogue waves phenomenon [ ]. Wright III [ ] has obtained an auto-Bäklund transformation for plane-wave solutions of a system of coupled long-waveshort-wave equations by using the dressing method. By using the above transformation, the original equation can be converted into Hirota’s bilinear form, G(Dt, Dx; f ) = , where the D-operator is defined by [ ]. We solve the above bilinear differential equations to get breather wave solutions by using a two-soliton method with the help of MAPLE. ) can be rewritten as the following coupled bilinear differential equations for F, G, and H:. ) can be converted into the solutions of coupled bilinear differential equations ). The two-soliton solutions of bilinear differential equations can be expressed in the form. We report the explicit forms of these breather solutions

Various breathers of the coupled long-wave-short-wave system

Conclusion and discussion