On the optimal conditions for the focusing of giant sea waves
- 41 Downloads
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.
KeywordsWave Packet JETP Letter Rogue Wave Nonlinear Regime Freak Wave
Unable to display preview. Download preview PDF.