English

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 2×22\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.

Keywords

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

R2 v1 2026-07-22T18:15:13.142Z