Contents Online
Communications in Mathematical Sciences
Volume 2 (2004)
Number 1
Stablity of solitary waves in higher order Sobolev spaces
Pages: 35 – 52
DOI: https://dx.doi.org/10.4310/CMS.2004.v2.n1.a3
Authors
Abstract
The orbital stability of solitary waves has generally been established in Sobolev classes of relatively low order, such as $H^1$. It is shown here that at least for solitary-wave solutions of certain model equations, a sharp form of orbital stability is valid in $L^2$-based Sobolev classes of arbitrarily high order. Our theory includes the classical Korteweg-de Vries equation, the Benjamin- Ono equation and the cubic, nonlinear Schrödinger equation.
Published 1 January 2004