Determinant Structure of the Rational Solutions for the Painlev\'e II Equation

Doshisha Univ.); Hiroshima Univ.); Kenji Kajiwara (Dept. of Elect. Engin.; Yasuhiro Ohta (Dept. Appl. Math.

arxiv: solv-int/9607002 · v1 · submitted 1996-07-15 · solv-int · nlin.SI

Determinant Structure of the Rational Solutions for the Painlev\'e II Equation

Kenji Kajiwara (Dept. of Elect. Engin. , Doshisha Univ.) , Yasuhiro Ohta (Dept. Appl. Math. , Hiroshima Univ.) This is my paper

classification solv-int nlin.SI

keywords determinantsolutionsequationpainlevrationalrepresentationanotherbilinear

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Two types of determinant representations of the rational solutions for the Painlev\'e II equation are discussed by using the bilinear formalism. One of them is a representation by the Devisme polynomials, and another one is a Hankel determinant representation. They are derived from the determinant solutions of the KP hierarchy and Toda lattice, respectively.

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Determinant Structure of the Rational Solutions for the Painlev\'e II Equation

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