Integrable self-adaptive moving mesh schemes for multi-component short pulse type equations under general boundary conditions

TL;DR

This paper develops integrable self-adaptive moving mesh schemes for multi-component short pulse equations, enabling accurate numerical solutions with soliton features under various boundary conditions.

Contribution

It introduces a novel integrable self-adaptive moving mesh framework for multi-component short pulse equations using hodograph transformations.

Findings

Successfully constructed multi-soliton solutions expressed by Pfaffian.

Numerical experiments demonstrate the schemes' effectiveness and accuracy.

Applicable to general boundary conditions, including periodic.

Abstract

In this paper, we construct integrable self-adaptive moving mesh schemes for multi-component modified short pulse and short pulse equations under general boundary conditions including periodic boundary conditions by using the consistency condition with the hodograph transformation. We also construct multi-soliton solutions expressed by Pfaffian for our self-adaptive moving mesh schemes. Using self-adaptive moving mesh schemes presented in this paper, we perform numerical experiments to evaluate their effectiveness and accuracy as a numerical method.