Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

Anne de Bouarda1

a1 Laboratoire d'Analyse Numérique, Université Paris-Sud, Bâtiment 425, 91405 Orsay, France

Abstract

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

(Received April 10 1993)

(Revised May 24 1994)