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arxiv: 0806.3338 · v1 · submitted 2008-06-20 · 🧮 math-ph · math.MP

Slow passage through parametric resonance for a weakly nonlinear dispersive wave

classification 🧮 math-ph math.MP
keywords parametricsolutionnonlinearresonanceasymptoticbeforechangeconnection
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A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance.

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