Special Session 108: 

Stability and instability of solitary wave solutions for systems of nonlinear dispersive equations

Hongqiu CHEN
University of Memphis
USA
Co-Author(s):    Xiaojun Wang
Abstract:
Considered here is a system $$\partial_t u+\partial_xu-\partial_{xxt}u +\partial_x\partial_u H(u, v)=0, $$ $$\partial_t u+\partial_xu-\partial_{xxt}u +\partial_x \partial_v H(u, v)=0$$ of nonlinear dispersive equations, where $u=u(x,t), v=v(x, t)$ are real-valued functions, and $H$ is a homogeneous polynomial function of degree $p\geq 3.$ We present existence of explicit solitary wave solutions. A simple algebraic condition for stability of the explicit solitary wave solution is derived. Criteria for instability of explicit solitary wave solutions are obtained as well.