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arXiv · 1704.04016

On the nonlinear Schr\"odinger equation for waves on a nonuniform current

V. P. Ruban
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Abstract

A nonlinear Schr\"odinger 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.

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BibTeXRIS

V. P. Ruban. 2017-04-13. On the nonlinear Schr\"odinger equation for waves on a nonuniform current. https://doi.org/10.1134/s002136401209010x

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