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A Note on Resonance and Nonlinear Dispersive Waves

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The general theory for the slow dispersion of nonlinear wave trains, first studied by Whitham, is applied to a wave train, which, in the weakly nonlinear limit, exhibits resonant singularities. Numerical and perturbation methods are used to develop singly periodic solutions both away from and near all such critical values. Similarly, the equations governing the slow modulations of such a system are found by asymptotic analysis. The expansions are found to be valid so long as the wave train is sufficiently nonlinear. These ideas should be applicable to other problems where resonant singularities arise, in particular, multiphase modes.
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Document Type: Research Article

Affiliations: Clarkson College of Technology

Publication date: March 1, 1975

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