Nonlinear modulational instabililty of the Stokes waves in 2d full water waves

Gong Chen; Qingtang Su

arxiv: 2012.15071 · v1 · pith:PSV7WXQJnew · submitted 2020-12-30 · 🧮 math.AP

Nonlinear modulational instabililty of the Stokes waves in 2d full water waves

Gong Chen , Qingtang Su This is my paper

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keywords wavesstokeswaterfullmodulationalnonlinearsystemunder

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The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly unstable under long-wave perturbations. Our approach is based on the modulational approximation of the water wave system and the instability mechanism of the focusing cubic nonlinear Schr\"odinger equation.

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