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arXiv · 1712.00485

Numerical approximation to Benjamin type equations. Generation and stability of solitary waves

Vassilios A. Dougalis·Angel Duran·Dimitrios Mitsotakis
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Abstract

This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge-Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves.

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Vassilios A. Dougalis, Angel Duran, Dimitrios Mitsotakis. 2017-12-01. Numerical approximation to Benjamin type equations. Generation and stability of solitary waves. https://arxiv.org/abs/1712.00485

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