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Titlebook: Important Developments in Soliton Theory; A. S. Fokas,V. E. Zakharov Book 1993 Springer-Verlag Berlin Heidelberg 1993 Eigenvalue.Hamiltoni

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The Isomonodromy Method and the Painlevé Equations the extension of the inverse spectral method from PDE’s to ODE’s. This method, which can be thought of as a nonlinear analogue of the Laplace’s method for solving linear ODE’s, allows one to investigate the asymptotic behavior of the solutions of Painlevü transcendents and to obtain connection form
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The Inverse Spectral Method on the Planeociated linear eigenvalue equation. This inverse problem can be formulated as a Riemann-Hilbert (RH) problem. This formulation expresses the important fact that the underlying eigenfunction is sectionally meromorphic.
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