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


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.


Surface Tension Soliton Solitary Wave Euler Equation Wave Solution 
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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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