Numerical Analysis and Approximate Travelling Wave Solutions for a Higher Order Internal Wave System

W. C. Lesinhovski, A. Ruiz de Zárate

Abstract


In this work we focus on the numerical solution of a higher order bidirectional nonlinear model of Boussinesq type involving a nonlocal operator. Based on a von Neumann stability analysis for the linearized problem, an efficient and stable scheme for the nonlinear system is proposed. Our method is based on a numerical scheme known from the literature that solves satisfactorily a lower order linear system. Additionally, approximate periodic travelling wave solutions profiles for the higher order nonlinear system are presented. Such approximate travelling wave solutions are obtained from a solitary wave family of solutions for the Intermediate Long Wave (ILW) equation and the regularized Intermediate Long Wave (rILW) equation.


Keywords


Spectral method; Dispersive models; Stability analysis; Travelling waves

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DOI: https://doi.org/10.5540/tcam.2022.023.01.00079

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Trends in Computational and Applied Mathematics

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