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

TL;DR

This paper uses advanced numerical methods to generate and analyze the stability of solitary waves in generalized Benjamin equations, providing insights into their dynamics and interactions.

Contribution

It introduces a modified Petviashvili method with extrapolation for accurate solitary wave generation and employs spectral and Runge-Kutta methods for stability analysis.

Findings

Successful generation of solitary-wave profiles

Numerical evidence of wave stability under perturbations

Insights into solitary wave interactions

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.