Solutions of Analogs of Time-Dependent Schrödinger Equations Corresponding to a Pair of $$H^{2+2+1}$$ Hamiltonian Systems in the Hierarchy of Degenerations of an Isomonodromic Garnier System

Abstract

This paper continues a series of papers in which simultaneous \(2\times 2 \) matrix solutions of two scalar evolution equations, which are analogs of time-dependent Schrödinger equations, were constructed. In the constructions in the present paper, these equations correspond to the Hamiltonian system \(H^{2+2+1} \)—one of the representatives of the hierarchy of degenerations of the isomonodromic Garnier system. The mentioned hierarchy was described by H. Kimura in 1986. In terms of solutions of linear systems of differential equations in the method of isomonodromic deformations, the consistency condition for which is the Hamiltonian equations of the \(H^{2+2+1} \) system, the constructed simultaneous matrix solutions of analogs of time-dependent Schrödinger equations are written out explicitly in this paper.