Finite-Wavelength Stability¶of Capillary-Gravity Solitary Waves
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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.
KeywordsSurface Tension Soliton Solitary Wave Euler Equation Wave Solution
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