Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlev\'e hierarchy

Yusuke Sasano

Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlev\'e hierarchy

Algebraic Geometry 2012-08-08 v9 Mathematical Physics Classical Analysis and ODEs Dynamical Systems math.MP

Authors: Yusuke Sasano

Abstract

We find a one-parameter family of polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$ -symmetry. We also show that this system can be obtained by the compatibility conditions for the linear differential equations in three variables. We give a relation between it and the second member of the second Painlev\'e hierarchy. Moreover, we give some relations between an autonomous version of its polynomial Hamiltonian system in two variables and the mKdV hierarchies.

Keywords

polynomial Hamiltonian system W-symmetry Painlevé hierarchy compatibility conditions linear differential equations mKdV hierarchies autonomous systems

Cite

@article{arxiv.0806.2431,
  title  = {Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlev\'e hierarchy},
  author = {Yusuke Sasano},
  journal= {arXiv preprint arXiv:0806.2431},
  year   = {2012}
}

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29 pages, 2 figures

Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlev\'e hierarchy

Abstract

Keywords

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