Finite-Wavelength Stability¶of Capillary-Gravity Solitary Waves |
| |
Authors: | Mariana Haragus Arnd Scheel |
| |
Institution: | Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence Cedex, France. E-mail: haragus@math.u-bordeaux.fr, FR Institut für Mathematik I, Freie Universit?t Berlin, Arnimallee 2–, 14195 Berlin, Germany, DE
|
| |
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.
Received: 7 February 2001 / Accepted: 6 October 2001 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|