Stability of solitary waves for a nonlinearly dispersive equation

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July 2004, 10(3): 709-717. doi: 10.3934/dcds.2004.10.709

Stability of solitary waves for a nonlinearly dispersive equation

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

Received December 2002 Revised May 2003 Published January 2004

Abstract
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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.

Keywords: orbital stability, Solitary waves, nonlinear dispersion..

Mathematics Subject Classification: 35B35, 35G2.

Citation: H. Kalisch. Stability of solitary waves for a nonlinearly dispersive equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 709-717. doi: 10.3934/dcds.2004.10.709

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