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Abstract <p> The present paper is devoted to the construction of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(2\times2\)</EquationSource> </InlineEquation> joint matrix solutions of two pairs of scalar evolution equations, which are analogs of nonstationary Schrödinger equations. Every pair of these analogs of the Schrödinger equations corresponds to one of two pairs of joint isomonodromic Hamiltonian systems <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H^{5/2+3/2}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(H^{5/2+2}\)</EquationSource> </InlineEquation>, which are representatives of the hierarchy of degenerations of the Garnier system. These two pairs of isomonodromic systems are contained in the 2009 paper by H. Kawamuko in which the hierarchy of degenerations of the Garnier system, described earlier by H. Kimura, was supplemented. The constructed joint matrix solutions of the analogs of nonstationary Schrödinger equations in this paper are explicitly written out in terms of solutions of linear systems of differential equations by isomonodromic deformation methods whose conditions are pairs of Hamiltonian systems <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(H^{5/2+3/2}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(H^{5/2+2}\)</EquationSource> </InlineEquation>. </p>

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Construction of Solutions to Analogs of Nonstationary Schrödinger Equations Corresponding to a Pair of Isomonodromic Hamiltonian Systems \(H^{5/2+3/2}\) and \(H^{5/2+2}\) of the Hierarchy of Degenerations of the Garnier System

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  • 发表日期：

    2025年8月1日

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  • V. A. Pavlenko

摘要

Abstract

The present paper is devoted to the construction of \(2\times2\) joint matrix solutions of two pairs of scalar evolution equations, which are analogs of nonstationary Schrödinger equations. Every pair of these analogs of the Schrödinger equations corresponds to one of two pairs of joint isomonodromic Hamiltonian systems \(H^{5/2+3/2}\) and \(H^{5/2+2}\) , which are representatives of the hierarchy of degenerations of the Garnier system. These two pairs of isomonodromic systems are contained in the 2009 paper by H. Kawamuko in which the hierarchy of degenerations of the Garnier system, described earlier by H. Kimura, was supplemented. The constructed joint matrix solutions of the analogs of nonstationary Schrödinger equations in this paper are explicitly written out in terms of solutions of linear systems of differential equations by isomonodromic deformation methods whose conditions are pairs of Hamiltonian systems \(H^{5/2+3/2}\) and \(H^{5/2+2}\) .