Nonlinear Modulated Gravity Wave on a Liquid Layer with Random Inhomogeneous Depth

Abstract

Nonlinear modulated gravity wave on a liquid layer with random inhomogeneous depth is investigated for a case of long wavelength. By means of nonlinear perturbation method, a modified form of the nonlinear Schrödinger equation for a complex amplitude of the wave is derived. It is shown that the randomness of the depth not only causes amplitude damping and shifts of wavelength and phase velocity but also destroys the periodicity of a nonlinear wave train.