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
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引用次数: 0
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.
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.在本文的构造中，这些方程对应于哈密顿系统（H^{2+2+1} \）--等单调伽尼耶系统退化层次的代表之一。上述层次结构由 H. Kimura 在 1986 年描述。木村（Kimura）于 1986 年描述了上述层次结构。在等单旋转变形方法中的线性微分方程系的解方面，其一致性条件是 \(H^{2+2+1} \)系统的哈密顿方程，本文明确写出了构建的时变薛定谔方程类似物的同步矩阵解。
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