Painlev\'e Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System

TL;DR

This paper investigates the integrability of a variable coefficient coupled HI mKdV system with shifted nonlocal reductions, establishing conditions for integrability and exploring the effects of shifted symmetries on soliton solutions.

Contribution

It introduces a method to analyze integrability via the Weiss Tabor Carnevale test and demonstrates how shifted symmetries influence the system's soliton structure.

Findings

Coefficient restrictions for integrability identified

Time reparametrization to achieve autonomous form

Shifted symmetries create new symmetry centers without altering soliton shape

Abstract

We analyze a variable coefficient coupled HI mKdV system that has shifted nonlocal reductions. The Weiss Tabor Carnevale test gives us coefficient restrictions to perform a time reparametrization to achieve an autonomous integrable model. We also show a Hirota bilinear form along with a simplified example to demonstrate how the shifted symmetries create new symmetry centers, but do not affect the shape of the soliton.