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Similarity reduction of the modified Yajima-Oikawa equation

Tetsuya Kikuchi·Takeshi Ikeda·Saburo Kakei
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Abstract

We study a similarity reduction of the modified Yajima-Oikawa hierarchy. The hierarchy is associated with a non-standard Heisenberg subalgebra in the affine Lie algebra of type A_2^{(1)}. The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom two, and admits a group of Bäcklund transformations isomorphic to the affine Weyl group of type A_2^{(1)}. We show that the system is equivalent to a two-parameter family of the fifth Painlevé equation.

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Tetsuya Kikuchi, Takeshi Ikeda, Saburo Kakei. 2003-09-16. Similarity reduction of the modified Yajima-Oikawa equation. https://doi.org/10.1088/0305-4470%2F36%2F45%2F008

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