Two-component soliton systems and the Painlev\'e equations

Mikio Murata

Two-component soliton systems and the Painlev\'e equations

可精确求解与可积系统 2011-11-10 v2

作者: Mikio Murata

摘要

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.

关键词

integrable hierarchies painlevé equations and orthogonal polynomials soliton

引用

@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}
}

备注

39 pages

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