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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Nonlinear Dispersive Equations
Solitary Waves
Solitons
Traveling Wave
Surface Waves
Extremum
Hamiltonian Systems
Hamiltonians
Gravity
Partial differential equation
Unstable
Differential equation
Necessary Conditions
Surface waves
Partial differential equations
Gravitation
Differential equations
Energy
Class

Cite this

A stability result for solitary waves in nonlinear dispersive equations. / Akers, B; Milewski, Paul A.

In: Communications in Mathematical Sciences, Vol. 6, No. 3, 09.2008, p. 791-797.

Research output: Contribution to journalArticle

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