Finite-wavelength stability of capillary-gravity solitary waves
نویسندگان
چکیده
We consider the Euler equations describing nonlinear waves on the free surface of a twodimensional 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 in the long-wavelength regime, where a Boussinesqequation governs the dynamics, and unstable eigenvalues arising from non-adiabatic interaction of the infinite-wavelength soliton with finite-wavelength perturbations.
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