Painlevé Equation, Reflection Groups and τ -Functions

Author: Kholoud Bakhat S Alzahrani

Alzahrani, Kholoud Bakhat S, 2020 Painlevé Equation, Reflection Groups and τ -Functions, Flinders University, College of Science and Engineering

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The aim of this research is clarify the special algebraic solutions of the Painlevé equations using the Weyl groups via the explicit example of the forth Painlevé equation which admits the Weyl group symmetry of type A2. We do so via an important object called τ-functions which is defined from the Hamiltonian representation of the Painlevé equation.

Keywords: Painlevé Equation, Weyl group, Hamiltonian representation and τ -Functions

Subject: Mathematical Sciences thesis

Thesis type: Masters
Completed: 2020
School: College of Science and Engineering
Supervisor: Yang Shi