Dynamical understanding of loop soliton solution for several nonlinear wave equations  

作　　者：Ji-bin LI Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China Kunming University of Science and Technology, Kunming 650093, China 

出　　处：《Science China Mathematics》2007年第6期773-785,共13页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10671179);the Natural Science Foundation of Yunnan Province (Grant No. 2005A0013M)

摘　　要：It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.

关 键 词：planar dynamical system homoclinic orbit solitary wave solution one-loop soliton solution periodic wave solution bifurcation nonlinear wave equation 34C37 34C23 74J30 58Z05 

分 类 号：O175.29[理学—数学]