JETP Letters

, Volume 100, Issue 11, pp 751–755 | Cite as

On the optimal conditions for the focusing of giant sea waves

  • V. P. Ruban
Nonlinear Dynamics


The dynamics of a wave packet on a two-dimensional sea surface, which is described by the nonlinear Schröbinger equation 2iψ t + ψ xx − ψ yy + |ψ|2ψ = 0, has been analyzed within the Gaussian variational ansatz in application to the problem of the formation of rogue waves. The longitudinal (X(t)) and transverse (Y(t)) sizes of the packet are described by a system of differential equations: \(\ddot X = 1/X^3 - N/(X^2 Y)\) and \(\dddot Y = 1/Y^3 + N/(Y^2 X)\), where the parameter N is proportional to the integral of motion ∫|ψ|2 dxdy. This system is interated in quadratures at an arbitrary N value, which makes it possible to understand the linear and nonlinear regimes of the focusing of a wavepacket and to formulate the optimal initial conditions under which the amplitude of the wave at the maximum is much larger than that in the linear case.


Wave Packet JETP Letter Rogue Wave Nonlinear Regime Freak Wave 
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Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

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

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