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In mathematics, the equations governing the isomonodromic deformation of meromorphic linear systems of ordinary differential equations are, in a fairly precise sense, the most fundamental exact nonlinear differential equations. As a result, their solutions and properties lie at the heart of the field of exact nonlinearity and integrable systems. Isomonodromic deformations were first studied by Lazarus Fuchs, with early pioneering contributions from Paul Painlevé, René Garnier, and Ludwig Schlesinger. Inspired by results in statistical mechanics, a seminal contribution to the theory was made by Michio Jimbo, Tetsuji Miwa and Kimio Ueno, who studied cases with arbitrary singularity structure. ==Fuchsian systems and Schlesinger's equations== We consider the Fuchsian system of linear differential equations : where the independent variable ''x'' takes values in the complex projective line P1(C), the solution ''Y'' takes values in C''n'' and the ''Ai'' are constant ''n''×''n'' matrices. By placing ''n'' independent column solutions into a fundamental matrix we can regard ''Y'' as taking values in GL(''n'', C). Solutions to this equation have simple poles at ''x'' = λ''i''. For simplicity, we shall assume that there is no further pole at infinity which amounts to the condition that : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Isomonodromic deformation」の詳細全文を読む スポンサード リンク
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