Zero Curvature and generalization of Painlev\'e equation from AKNS/Lund-Regge model

TL;DR

This paper explores the connection between integrable models and Painlevé equations, proposing a new transcendental function through the mixed AKNS/Lund-Regge model and analyzing its properties.

Contribution

It introduces a novel approach linking AKNS/Lund-Regge models with Painlevé equations, including a perturbative test and local solution representation.

Findings

Identified a candidate system for a new transcendental function.

Applied Painlevé test to analyze integrability.

Provided local solution representation.

Abstract

We explain the relation between the mixed mKdV/sinh-Gordon model and the Kudryashov's equation. Then, we use the mixed AKNS/Lund-Regge model to find a system of ODEs which is candidate to define a new transcendental function. We also applied the perturbative Painlev\'e test and presented the local representation for the solution of the system.