Determinant Structure of the Rational Solutions for the Painlev\'e IV Equation
classification
solv-int
nlin.SI
keywords
solutionsdeterminantequationpainlevpolynomialsrationalschuranother
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Rational solutions for the Painlev\'e 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 determinant of the Hermite polynomials, or by special case of the Schur polynomials.
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