Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes

TL;DR

This paper develops spectral Fourier-Galerkin methods for numerically approximating internal-wave systems, specifically the Intermediate Long Wave and Benjamin-Ono models, and improves solitary wave computation techniques.

Contribution

It introduces a spectral Fourier-Galerkin discretization for these wave systems and enhances solitary wave generation with acceleration methods.

Findings

Error analysis of semidiscretizations

Effective numerical generation of solitary waves

Validation through numerical examples

Abstract

The paper is concerned with the numerical approximation of the Intermediate Long Wave and Benjamin-Ono systems, that serve as models for the propagation of interfacial internal waves in a two-layer fluid system in particular physical regimes. The paper focuses on two issues of approximation. First, the spectral Fourier-Galerkin method is used to discretize in space the corresponding periodic initial-value problems, and the error of the semidiscretizations is analyzed. The second issue concerns the numerical generation of solitary-wave solutions of the systems. We use acceleration techniques to improve the computation of the approximate solitary waves and check their performance with numerical examples.