Construction of solutions of analogs of the Schrodinger time equations corresponding to the Hamiltonian system H²⁺²⁺¹

2023/04/13 by Pavlenko, V. A.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2304.07631

Abstract

This paper continues a series of papers in which 2-by-2 matrix joint solutions of two scalar evolutionary equations are constructed, which are analogs of the Schrodinger time equations. These equations correspond to the Hamiltonian system H²⁺²⁺¹, being 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 ordinary differential equations of the method of isomnodromic deformations, the compatibility condition of which are the Hamiltonian equations of the system H²⁺²⁺¹, the constructed joint matrix solutions of analogs of the time equations of the Schrodinger equations in this paper will be written out explicitly.

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