Similarity reduction of the modified Yajima-Oikawa equation

Details Similarity reduction of the modified Yajima-Oikawa equation Similarity reduction of the modified Yajima-Oikawa equation

2003-04-14

arxiv.org/abs/nlin/0304024v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

latex2e file, 18 pages, no figures; (v2)Introduction is modified. Some typos are corrected

Scientific paper

10.1088/0305-4470/36/45/008

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 B\"acklund 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 Painlev\'e equation.

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