A stability result for solitary waves in nonlinear dispersive equations

The stability of solitary traveling waves in a general class of conservative nonlinear dispersive equations is discussed. A necessary condition for the exchange of stability of traveling waves is presented; an unstable eigenmode may bifurcate from the neutral translational mode only at relative extrema of the wave energy. This paper extends a result from Hamiltonian systems, and from a few integrable partial differential equations, to a broader class of conservative differential equations, with particular application to gravity-capillary surface waves.

Keywords

stability, solitary wave, gravity-capillary wave

2010 Mathematics Subject Classification

76B15, 76B25, 76B45

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Published 1 January 2008