A Symmetric System of Mixed Painleve III - V Equations and its Integrable Origin

TL;DR

This paper introduces a new mixed symmetric Painleve III - V model derived from an integrable 4-boson hierarchy, expanding the understanding of integrable systems and their interrelations.

Contribution

It presents a novel hybrid Painleve III - V system obtained through self-similarity and Dirac reduction techniques from an integrable hierarchy.

Findings

Derived a symmetric mixed Painleve III - V equation

Connected the model to an underlying integrable hierarchy

Provided a framework for analyzing hybrid Painleve systems

Abstract

A mixed symmetric Painleve III - V model which describes a hybrid of both equations is defined and obtained by successive self-similarity and Dirac Lagrange multiplier reductions from an integrable 4-boson hierarchy.