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

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 includ...

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Bibliographic Details
Published in:Wave motion 2019-01, Vol.85, p.34-56
Main Authors: Dougalis, V.A., Duran, A., Mitsotakis, D.
Format: Article
Language:English
Subjects:
Benjamin type equations
Collocation methods
Fourier transforms
Numerical analysis
Propagation
Runge-Kutta method
Solitary waves
Spectral method
Stability
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Summary: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. •A numerical method for Benjamin type equations is introduced.•Accuracy and stability properties are shown.•Evolution properties are validated with solitary wave simulations.•Collisions and stability properties of solitary waves are studied.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2018.11.002