Journal Article10.1016/0167-2789(81)90021-X
Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II
Michio Jimbo,Tetsuji Miwa +1 more
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TL;DR: In this article, a series of τ functions parametrized by integers are introduced and their ratios to the original τ function are then shown to be explicit rational expressions in terms of the coefficients of A(x).
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About: This article is published in Physica D: Nonlinear Phenomena. The article was published on 01 Jun 1981. The article focuses on the topics: Monodromy & Homogeneous differential equation.
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Citations
An Isomonodromy Cluster of Two Regular Singularities
TL;DR: In this paper, a linear ODE with two coalescing regular singularities is considered, and the coalescence process is restricted with an isomonodromy condition with respect to the distance between the merging singularities in a way consistent with the ODE.
Poles of Painlevé IV Rationals and their Distribution
Davide Masoero,Pieter Roffelsen +1 more
TL;DR: In this paper, the authors studied the distribution of singularities of rational solutions of the Painleve IV equation by means of the isomonodromic deformation method, where singularities are expressed in terms of the roots of generalised Hermite and generalised Okamoto polynomials.
Biorthogonal Systems on the Unit Circle, Regular Semiclassical Weights, and the Discrete Garnier Equations
TL;DR: In this paper, it was shown that a system of biorthogonal polynomials and their associated functions corresponding to a regular semiclassical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by explicitly constructing its Hamiltonian formulation, and showing that it coincides with that of a Garnier system.
References
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TL;DR: In this paper, a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable is presented.
Non-linear equations of korteweg-de vries type, finite-zone linear operators, and
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TL;DR: In this article, a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable is presented.
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