Small-amplitude plane internal waves in the 2D inviscid Boussinesq system are proven to be spectrally unstable via a rigorous Floquet-Bloch analysis.
Small-amplitude finite-depth Stokes waves are transversally unstable
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We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.
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Instabilities of internal gravity waves in the two-dimensional Boussinesq system
Small-amplitude plane internal waves in the 2D inviscid Boussinesq system are proven to be spectrally unstable via a rigorous Floquet-Bloch analysis.