Tau Functions of the Fourth Painlevé Equation in Two Variables

MR2154382 Tsuda, Teruhisa Teruhisa TSUDA Tau Functions of the Fourth Painlevé Equation in Two Variables Funkcialaj Ekvacioj. Serio Internacia 48 2005 137--145 http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-1/48_137.pdf http://www.ams.org/mathscinet-getitem?mr=MR2154382 We investigate the solutions of the fourth Painlevé equation in two variables by means of tau functions. Hirota bilinear forms and birational symmetries of the equation are presented. We obtain in particular a complete description of the rational solutions in terms of Schur polynomials. Painlevé equation, Garnier system, Schur polynomial. 33E17, 37K10, 05E05. 48-137 2005 Tau Functions of the Fourth Painlevé Equation in Two Variables TSUDA, Teruhisa Teruhisa TSUDA

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