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

Abstract

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 Schrödinger equation.

References in corpus (5)

• A blow-up criteria and the existence of 2d gravity water waves with angled crests
• On a class of self-similar 2D surface water waves
• The quartic integrability and long time existence of steep water waves in 2D
• On the transition of the Rayleigh-Taylor instability in 2d water waves
• The Benjamin-Feir instability in the infinite depth

Cited by in corpus (1)

• Full description of Benjamin-Feir instability of Stokes waves in deep water