Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves

Details Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves

2012-03-21

arxiv.org/abs/1203.4735v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 3 figures

Scientific paper

We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS with constant coefficients. The transformation is valid as long as |{\Gamma}t| \ll 1, with {\Gamma} the growth/damping rate of the waves due to the wind/dissipation. Approximate rogue wave solutions of the equation are presented and discussed. The results shed some lights on the effects of wind and dissipation on the formation of rogue waves.

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