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Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
journal contributionposted on 17.06.2020, 22:04 by VA Dougalis, A Duran, Dimitrios MitsotakisDimitrios Mitsotakis
© 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.