A stability result for solitary waves in nonlinear dispersive equations

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Abstract

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.
Original languageEnglish
Pages (from-to)791-797
Number of pages7
JournalCommunications in Mathematical Sciences
Volume6
Issue number3
Publication statusPublished - Sep 2008

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