Tau-functions and special solutions in a coupled Painlevé system

Details Tau-functions and special solutions in a coupled Painlevé system Tau-functions and special solutions in a coupled Painlevé system

2002-09-13

arxiv.org/abs/nlin/0209030v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Poster from NEEDS 2001, Cambridge

Scientific paper

For a pair of coupled Painlev\'e equations obtained as a similarity reduction
of the Hirota-Satsuma systems we describe special parameter-families of
solutions given in terms of mixtures of rational and Airy functions, and in
terms of a second Painlev\'e transcendent. The tau-functions associated to some
of these solutions are also given explicitly.

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