Numerical approximation of solitary waves of the Benjamin equation

© 2018 Elsevier B.V. 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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Numerical approximation to Benjamin type equations. Generation and stability of solitary waves

Wave Motion ◽

10.1016/j.wavemoti.2018.11.002 ◽

2019 ◽

Vol 85 ◽

pp. 34-56 ◽

Cited By ~ 4

Author(s):

V.A. Dougalis ◽

A. Duran ◽

D. Mitsotakis

Keyword(s):

Solitary Waves ◽

Numerical Approximation ◽

Stability Of Solitary Waves

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

10.26686/wgtn.12501905.v1 ◽

2020 ◽

Author(s):

VA Dougalis ◽

A Duran ◽

Dimitrios Mitsotakis

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Numerical Approximation ◽

Solitary Wave Solutions ◽

Time Stepping ◽

Runge Kutta Method ◽

Stability Of Solitary Waves ◽

The Stability ◽

Numerical Generation ◽

The Waves

© 2018 Elsevier B.V. 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.

Download Full-text