Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations
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Publication:879657
DOI10.1007/BF03321618zbMath1112.33015MaRDI QIDQ879657
Publication date: 14 May 2007
Published in: Computational Methods and Function Theory (Search for Journal in Brave)
Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17)
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Generalized Hermite polynomials and monodromy-free Schrödinger operators ⋮ Recurrence relations for Wronskian Hermite polynomials ⋮ Approximation of zeros of generalized Hermite polynomials by modulated elliptic function ⋮ Rational solutions of the Painlevé-II equation revisited ⋮ A constructive proof for the Umemura polynomials of the third Painlevé equation ⋮ Rational solutions of a \((2+1)\)-dimensional Sharma-Tasso-Olver equation ⋮ A Fuchsian matrix differential equation for Selberg correlation integrals ⋮ Recurrence relations for Wronskian Laguerre polynomials ⋮ The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials ⋮ The generalized Yablonskii-Vorob'ev polynomials and their properties ⋮ Rational solutions of the Painlevé-III equation: large parameter asymptotics ⋮ Special polynomials related to the supersymmetric eight-vertex model: a summary ⋮ Vortices and Polynomials ⋮ Rational solutions of the classical Boussinesq system ⋮ Triangular Schlesinger systems and superelliptic curves ⋮ RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION ⋮ Wronskian Appell polynomials and symmetric functions ⋮ Exact boundaries for the analytical approximate solution of a class of first-order nonlinear differential equations in the real domain ⋮ Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method ⋮ On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials
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