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Determinant structure of the rational solutions for the Painlevé IV equation

Kenji Kajiwara-+ and Yasuhiro Ohta++

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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 determinants of the Hermite polynomials, or by a special case of the Schur polynomials.


PACS

02.10.De Algebraic structures and number theory

02.10.Ud Linear algebra

02.30.Ik Integrable systems

MSC

11C20 Matrices, determinants (See also 15A36)

17B80 Applications to integrable systems

15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)

Subjects

Mathematical physics

Dates

Issue 10 (13 March 1998)

Received 29 September 1997



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