IUMJ

Title: The Cauchy problem and the stability of solitary waves of a hyperelastic dispersive equation

Authors: Robin Ming Chen

Issue: Volume 57 (2008), Issue 5, 2377-2422

Abstract:

We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions $u(x,y,t) = phi_c(x - ct, y)$ that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it remains close to the set for all time in the natural norm.