Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves |
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Authors: | Miguel Onorato Davide Proment |
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Institution: | 1. Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy;2. INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy |
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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|?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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Keywords: | Rogue waves Water waves Breathers |
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