Two-component soliton systems and the Painlevé equations

Details Two-component soliton systems and the Painlevé equations Two-component soliton systems and the Painlevé equations

2006-03-31

arxiv.org/abs/nlin/0604001v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

39 pages

Scientific paper

We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear $2\times 2$ system by taking into consideration the hierarchy through a reduction procedure. The Lax pair of the Schlesinger system and the sixth Painlev\'e equation is given from this linear system. A unified approach to treat the other Painlev\'e equations from the usual two-component KP hierarchy is also considered.

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