Determinant Structure of the Rational Solutions for the Painlevé IV Equation

Abstract

Rational solutions for the Painlevé IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in another two hierarchies by Casorati determinant of the Hermite polynomials, or by special case of the Schur polynomials.

19 pages, Latex, using theorem.sty

References in corpus (1)

• Determinant Structure of the Rational Solutions for the Painlevé II Equation

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• Coefficients of Wronskian Hermite polynomials
• Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
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• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• Asymptotic behavior of Wronskian polynomials that are factorized via $p$-cores and $p$-quotients
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation