| Abstract: |
| We analyze the Benney model for interaction of short and long waves in resonant water wave interactions. Our particular interest is in the periodic traveling waves, which we construct and study in detail. The main results are that, for all natural values of the parameters, the periodic dnoidal waves are spectrally stable with respect to perturbations of the same period. For another natural set of parameters, we construct the snoidal waves, which exhibit instabilities, in the same setup. For the periodic travelling waves of the Zakharov system, we show that, for all natural values of the parameters, the dnoidal waves are spectrally stable with respect to perturbations of the same period. |
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