On the nonlinear Schrödinger equation for waves on a nonuniform current

Abstract

A nonlinear Schrödinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can describe with good accuracy the loss of modulation stability of a wave coming to a counter current, leading to the formation of so called rogue waves. Some theoretical estimates are compared to the numerical simulation with the exact equations for a two-dimensional potential motion of an ideal fluid with a free boundary over a nonuniform bottom at a nonzero average horizontal velocity.

6 pages, 10 figures, published in 2012

References in corpus (3)

• Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves
• "Breathing" rogue wave observed in numerical experiment
• Explicit equations for two-dimensional water waves with constant vorticity

Cited by in corpus (3)

• Wave amplification in the framework of forced nonlinear Schrodinger equation: the rogue wave context
• Nonlinear dynamics of trapped waves on jet currents and rogue waves
• Waves over Curved Bottom: The Method of Composite Conformal Mapping