Two-component soliton systems and the Painlevé equations

Abstract

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 Painlevé equation is given from this linear system. A unified approach to treat the other Painlevé equations from the usual two-component KP hierarchy is also considered.

39 pages

References in corpus (2)

• Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
• Higher order Painlevé equations of type $A_l^{(1)}$