2000 character limit reached
Nonlinear modulational instabililty of the Stokes waves in 2d full water waves (2012.15071v1)
Published 30 Dec 2020 in math.AP
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 Schr\"odinger equation.