UAH > Math > Colloquia > 8/31/2007

Dynamical Understanding of Loop Soliton Solutions for Several Nonlinear Wave Equations

Professor Jibin Li

Department of Mathematics, Kunming University of Science and Technology and
Department of Mathematics, Zhejiang Normal University, China

August 31, 2007
202 Madison Hall
2:45 - 3:45 (Refreshments at 2:15 in 201 Madison Hall)

Abstract

It is important to understand the dynamical behavior for the traveling wave solutions governed by singular traveling wave equations.

It had been found that some nonlinear wave equations have a one-loop soliton solution. What is the dynamical behavior of the so called one-loop soliton solution? To answer this question, traveling wave solutions for four nonlinear wave equations are discussed. Explicit parametric representations of some special traveling wave solutions are given. Our conclusion to the question is that the loop solution consists of three different breaking traveling wave solutions, and hence the so called "loop soliton solution" is actually not a real soliton solution.