Two-component soliton systems and the Painlev\'e equations
Exactly Solvable and Integrable Systems
2011-11-10 v2
Abstract
We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear 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.
Cite
@article{arxiv.nlin/0604001,
title = {Two-component soliton systems and the Painlev\'e equations},
author = {Mikio Murata},
journal= {arXiv preprint arXiv:nlin/0604001},
year = {2011}
}
Comments
39 pages