Stability of solitary waves for a nonlinearly dispersive equation

H. Kalisch

doi:10.3934/dcds.2004.10.709

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2004, Volume 10, Issue 3: 709-717. Doi: 10.3934/dcds.2004.10.709

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Stability of solitary waves for a nonlinearly dispersive equation

H. Kalisch^1,

1.
Centre for Mathematical Sciences, Lund University, 221 00 Lund

Received: December 2002

Revised: May 2003

Published: July 2004

Abstract / Introduction Related Papers Cited by

Abstract

Solitary-wave solutions of a nonlinearly dispersive equation are considered. It is found that solitary waves are peaked or smooth waves, depending on the wave speed. The stability of the smooth solitary waves also depends on the wave speed. Orbital stability is proved for some wave speeds, while instability is proved for others.

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Mathematics Subject Classification: 35B35, 35G25.

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