American Institute of Mathematical Sciences

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

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