Nonsingular positon and complexiton solutions for the coupled KdV system

Abstract

Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction solutions are also firstly found for S-integrable model. The new analytical positon, negaton and complexiton solutions of the coupled KdV system are given out both analytically and graphically by means of the iterative Darboux transformations.Comment: 16 pages, 8 figure

New Positon, Negaton, and Complexiton Solutions for a Coupled Korteweg–de Vries – Modified Korteweg–de Vries System

“…The positon for the potential f of the coupled KdVmKdV system is nonsingular, but the positon solutions for u and v are analytical when the constants in Lax pair (9) and (10) are fixed as c 1 = c 2 = c, d 1 = d 2 = ck and k ≤ 1, but singularities arise when k > 1. And the negaton solutions are all nonsingular.…”

“…Since then, many other coupled KdV systems are constructed such as the Ito system, the Nutku-Oguz model, and so on. Recently, new positon, negaton, and complexiton solutions for the two types of the coupled KdV system are presented by means of the Darboux transformation [9,10]. The analytical positon, negaton, and complexiton solutions for the coupled modified KdV (mKdV) system are given out directly in [11] from the zero seed solution by means of Darboux transformation.…”

He's variational method for a (2 + 1)-dimensional soliton equation

“…Exact solutions play a vital role in understanding various qualitative and quantitative features of nonlinear phenomena. There are diverse classes of interesting exact solutions, such as traveling wave solutions, but it often needs specific mathematical techniques to construct exact solutions due to the nonlinearity present in dynamics [2,3]. It has recently become more interesting to obtain exact solutions of nonlinear partial differential equations (NPDEs) using symbolic computation softwares such as Maple, Mathematica and Matlab that facilitate complex and tedious algebraical computations.…”

Component-trace identities for Hamiltonian structures

“…Such coupled systems of integrable couplings can also provide concrete examples of soliton equations exhibiting solution diversity (see, e.g. [35][36][37][38][39][40][41][42][43]). There remains, however, an open question [44].…”