A generalization of determinant formulas for the solutions of Painlevé II and XXXIV equations

Abstract

A generalization of determinant formulas for the classical solutions of Painlevé XXXIV and Painlevé II equations are constructed using the technique of Darboux transformation and Hirota's bilinear formalism. It is shown that the solutions admit determinant formulas even for the transcendental case.

20 pages, LaTeX 2.09(IOP style), submitted to J. Phys. A

References in corpus (1)

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

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• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation