JETP Letters

, Volume 95, Issue 9, pp 486–491

On the nonlinear Schrödinger equation for waves on a nonuniform current

Methods of Theoretical Physics

DOI: 10.1134/S002136401209010X

Cite this article as:
Ruban, V.P. Jetp Lett. (2012) 95: 486. doi:10.1134/S002136401209010X


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.

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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