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Numerical solution of nonlinear wave equations in stratified dispersive media. (English) Zbl 1092.76048

Summary: Nonlinear wave motion in dispersive media is solved numerically. The model applies to in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi-type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wave equations. In order to reduce the number of spatial grid points, a physically motivated quasi-envelope approach is introduced. The new method turns out to reduce the computational time significantly compared to the standard leap-frog scheme.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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References:

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