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On the nonlinear Schrödinger equation for waves on a nonuniform current

  • Methods of Theoretical Physics
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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.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 119334, Russia

    V. P. Ruban

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  1. V. P. Ruban
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Correspondence to V. P. Ruban.

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Original Russian Text © V.P. Ruban, 2012, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 95, No. 9, pp. 550–556.

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Ruban, V.P. On the nonlinear Schrödinger equation for waves on a nonuniform current. Jetp Lett. 95, 486–491 (2012). https://doi.org/10.1134/S002136401209010X

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  • DOI: https://doi.org/10.1134/S002136401209010X

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