Finite-wavelength stability of capillary-gravity solitary waves

Mariana Haragus, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We consider the Euler equations describing nonlinear waves on the free surface of a two-dimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1/3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with respect to perturbations of finite wave-number. In particular, we exclude possible unstable eigenvalues of the linearization at the soliton in the long-wavelength regime, corresponding to small frequency, and unstable eigenvalues with finite but bounded frequency, arising from non-adiabatic interaction of the infinite-wavelength soliton with finite-wavelength perturbations.

Original languageEnglish (US)
Pages (from-to)487-521
Number of pages35
JournalCommunications in Mathematical Physics
Volume225
Issue number3
DOIs
StatePublished - Jan 1 2002

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