Analytical and numerical solution of a transport equation for resonantly interacting waves in MHD for a van dar Waals gas

TL;DR

This paper presents an analytical and numerical analysis of resonant wave interactions in magnetohydrodynamics (MHD) for a van der Waals gas, focusing on soliton formation influenced by physical parameters.

Contribution

It derives a new evolution equation incorporating dispersion, nonlinearity, and convolution terms for resonant MHD wave interactions in a van der Waals gas.

Findings

Van der Waals parameter affects soliton structure.

Magnetic field influences wave interaction dynamics.

Dispersive effects are significant in wave evolution.

Abstract

In this paper, we characterized an analytical and numerical study of the resonant interaction between waves in MHD. A system of evolution equations is derived; we focus on the study of the interaction between a selected triad. The resulting evolution equation contains a dispersive term in addition to the nonlinear term and convolution term. Effects of the influence of van der Waals parameter and magnetic field on the formation and structure of solitons are studied.