完全非线性色散K(k,m+n)方程新的紧致子,孤子和孤波斑图解(英文)

Fully Nonlinear Dispersion K(k,m+n) Equations with New Compactons,Solitons and Solitary Patterns Solutions

本文以完全非线性色散K(k,m+n)方程ut+a(uk)x+b(um(un)xx)x=0为例,说明了一种映射法的应用.在m,n,k,a和b的多种不同取值情况下,获得了K(k,m+n)方程,几种新的紧致子,孤子,孤波斑图解.发现K(k,m+n=1)方程在某些条件下,不管会聚情况,还是发散情况,都存在紧致子。

In this paper,we choose the fully nonlinear dispersive K（k,m＋n） equations： ut＋u（uk）x＋b（um（un）xx）x=0 to illustrate the application of the new mapping method.We derive several new compacton,soliton,solitary pattern and periodic wave solutions of the K（k,m＋n） equations for all possible values of k,m,n,a and b,and find that the K（k,m＋n=1） equation exhibit compactons not only for focusing branch but also for the defocusing branch in some cases.