Classical solutions of the degenerate Garnier system and their coalescence structures

TL;DR

This paper explores solutions to the degenerate Garnier system, a generalization of the fifth Painlevé equation, presenting classical transcendental and algebraic solutions and analyzing their coalescence structures.

Contribution

It introduces two classes of particular solutions for the degenerate Garnier system and investigates their coalescence structures, expanding understanding of this system.

Findings

Identified classical transcendental solutions

Constructed algebraic solutions

Analyzed coalescence structures of solutions

Abstract

We study the degenerate Garnier system which generalizes the fifth Painlev\'{e} equation. We present two classes of particular solutions, classical transcendental and algebraic ones. Their coalescence structure is also investigated.