On the optimal conditions for the focusing of giant sea waves
Abstract
The dynamics of a wave packet on a two-dimensional sea surface, which is described by the nonlinear Schröbinger equation 2 iψ 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: and , 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.
- Publication:
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Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- February 2015
- DOI:
- 10.1134/S0021364014230106
- Bibcode:
- 2015JETPL.100..751R