PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Victor Nistor, Hope Shaffer, Ludmil Zikatanov.

Title:On the studies of the singular travelling waves equations: dynamical system approach
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Professor Jibin Li, KMUST, China
Abstract:
Nonlinear wave phenomena are of great importance in the physical world and have been for a long time a challenging topic of research for both pure and applied mathematicians. There are numerous nonlinear evolution equations for which we need to analyze the properties of the solutions for time evolution of the system. As the first step, we should understand the dynamics of their traveling wave solutions. There exists an enormous literature on the study of nonlinear wave equations, in which exact explicit solitary wave, kink wave, periodic wave solutions, bifurcations and dynamical stabilities of these waves are discussed. To find exact traveling wave solutions for a given nonlinear wave system, a lot of methods have been developed such as the inverse scattering method, Darboux transformation method, Hirota bilinear method, algebraic-geometric method, tanh method, etc. What is the dynamical behavior of these exact traveling wave solutions? How do the travelling wave solutions depend on the parameters of the system? What is the reason of the smoothness change of traveling wave solutions? How to understand the dynamics of the so-called compacton and peakon solutions? These are very interesting and important problems. In recent years, these topics have seen significant advances and research is also very active. The aim of this talk is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions with an emphasis on singular waves and understand their dynamics for some classes of the well-posedness of nonlinear evolution equations.

Room Reservation Information

Room Number:MB106
Date:04 / 16 / 2012
Time:02:30pm - 03:30pm