On a Dirichlet boundary value problem for an Ermakov–Painlevé I equation. A Hamiltonian EPI system

Abstract

Here, a proto-type Ermakov–Painlevé I equation is introduced and a homogeneous Dirichlet-type boundary value problem analysed. In addition, a novel Ermakov–Painlevé I system is set down which is reducible by an involutory transformation to the autonomous Ermakov–Ray–Reid system augmented by a single component Ermakov–Painlevé I equation. Hamiltonian such systems are delimited.

Keywords

• ermakov
• painlevé
• dirichlet boundary value problem
• hamiltonian system.