Stability of solitary waves for a nonlinearly dispersive equation | Zendy

Henrik Kalisch | Zendy

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Stability of solitary waves for a nonlinearly dispersive equation

Author(s) -

Henrik Kalisch

Publication year - 2004

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2004.10.709

Subject(s) - physics , stability (learning theory) , dispersive partial differential equation , instability , mechanical wave , wave speed , wave propagation , wave equation , dispersion (optics) , longitudinal wave , classical mechanics , mechanics , mathematical analysis , mathematics , optics , nonlinear system , quantum mechanics , computer science , machine learning

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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