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Communications in Mathematical Physics

, Volume 225, Issue 3, pp 487–521 | Cite as

Finite-Wavelength Stability¶of Capillary-Gravity Solitary Waves

  • Mariana Haragus
  • Arnd Scheel

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.

Keywords

Surface Tension Soliton Solitary Wave Euler Equation Wave Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mariana Haragus
    • 1
  • Arnd Scheel
    • 2
  1. 1.Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence Cedex, France. E-mail: haragus@math.u-bordeaux.frFR
  2. 2.Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2–, 14195 Berlin, GermanyDE

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