Similarity reduction of the modified Yajima-Oikawa equation

Tetsuya Kikuchi; Takeshi Ikeda; Saburo Kakei

doi:10.1088/0305-4470/36/45/008

Similarity reduction of the modified Yajima-Oikawa equation

Tetsuya Kikuchi^*, Takeshi Ikeda, Saburo Kakei

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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 A₂⁽¹⁾The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom 2, and admits a group of Bäcklund transformations isomorphic to the affine Weyl group of type A₂⁽¹⁾. We show that the system is equivalent to a two-parameter family of the fifth Painlevé equation.

Original language	English
Pages (from-to)	11465-11480
Number of pages	16
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	45
DOIs	https://doi.org/10.1088/0305-4470/36/45/008
Publication status	Published - 2003 Nov 14
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/36/45/008

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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 A2(1)The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom 2, and admits a group of B{\"a}cklund transformations isomorphic to the affine Weyl group of type A2(1). We show that the system is equivalent to a two-parameter family of the fifth Painlev{\'e} equation.",

author = "Tetsuya Kikuchi and Takeshi Ikeda and Saburo Kakei",

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AU - Kikuchi, Tetsuya

AU - Ikeda, Takeshi

AU - Kakei, Saburo

PY - 2003/11/14

Y1 - 2003/11/14

N2 - 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 A2(1)The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom 2, and admits a group of Bäcklund transformations isomorphic to the affine Weyl group of type A2(1). We show that the system is equivalent to a two-parameter family of the fifth Painlevé equation.

AB - 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 A2(1)The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom 2, and admits a group of Bäcklund transformations isomorphic to the affine Weyl group of type A2(1). We show that the system is equivalent to a two-parameter family of the fifth Painlevé equation.

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JO - Journal of Physics A: Mathematical and Theoretical

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IS - 45

ER -

Similarity reduction of the modified Yajima-Oikawa equation

Abstract

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