Communications in Mathematical Sciences

Volume 2 (2004)

Number 1

Stablity of solitary waves in higher order Sobolev spaces

Pages: 35 – 52

DOI: http://dx.doi.org/10.4310/CMS.2004.v2.n1.a3

Authors

Jerry L. Bona

Yue Liu

Nghiem V. Nguyen

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.

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