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.

arXiv comment6 pages, 10 figures, published in 2012

References in corpus (8)

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Cited by in corpus (4)

• The excitation of rogue waves in a variable medium: an experimental study on the interaction of water waves and currents
• 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