Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 72, pp. 1-18.

Title: Stability of solitary wave solutions for 
       equations of short and long dispersive waves

Author: Jaime Angulo Pava (UNICAMP, Sao Paulo, Brazil)
	 
Abstract: 
 In this paper, we consider the existence and stability of
 a novel set of solitary-wave solutions for two models of short
 and long dispersive waves in a two layer fluid.
 We prove the existence of solitary waves via the
 Concentration Compactness Method.  We then introduce the sets of
 solitary waves obtained through  our analysis for each model and
 we show that them are stable provided the associated action is
 strictly convex. We also establish the existence of intervals of
 convexity for each associated action. Our analysis does not depend
 of spectral conditions.
 
Submitted May 30, 2005. Published July 10, 2006.
Math Subject Classifications: 35Q35, 35Q53, 35Q55, 35B35, 58E30, 76B15.
Key Words: Dispersive wave equations; variational methods;
           stability; solitary wave solutions.