Determinant Structure of the Rational Solutions for the Painlevé II Equation

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

1996-07-15

arxiv.org/abs/solv-int/9607002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages LaTeX. To appear in J. Math. Phys.(1996)

Scientific paper

10.1063/1.531648

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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