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arXiv · 1203.4735

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

Miguel Onorato·Davide Proment
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Abstract

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 Schrödinger (NLS) equation into the standard NLS with constant coefficients. The transformation is valid as long as |Γt| \ll 1, with Γ 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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Miguel Onorato, Davide Proment. 2012-03-21. Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves. https://doi.org/10.1016/j.physleta.2012.05.063

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