Quadratic equations and monodromy evolving deformations

TL;DR

This paper develops a foundational theory on monodromy evolving deformations, linking it to quadratic systems and generalizing previous work on the DH-V system, with implications for understanding complex differential equations.

Contribution

It introduces a basic theory on monodromy evolving deformations and demonstrates its application to Halphen's second quadratic system, extending prior research.

Findings

Halphen's second quadratic system described by monodromy evolving deformations

Generalization of the DH-V system work by Chakravarty and Ablowitz

Establishment of a theoretical framework for monodromy evolving deformations

Abstract

We give a basic theory on monodromy evolving deformations. proposed by Chakravarty and Ablowitz in 1996. We show that Halphen's second quadratic system can be described by monodromy evolving deformations. Our result is a generalization of the work on the DH-V system by Chakravarty and Ablowitz.