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Affine Lie group approach to a derivative nonlinear Schrödinger equatoin and its similarity reduction

Saburo Kakei·Tetsuya Kikuchi
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Abstract

The generalized Drinfel'd-Sokolov hierarchies studied by de Groot-Hollowood-Miramontes are extended from the viewpoint of Sato-Wilson dressing method. In the A_1^(1) case, we obtain the hierarchy that include the derivative nonlinear Schrödinger equation. We give two types of affine Weyl group symmetry of the hierarchy based on the Gauss decomposition of the A_1^(1) affine Lie group. The fourth Painlevé equation and their Weyl group symmetry are obtained as a similarity reduction. We also clarify the connection between these systems and monodromy preserving deformations.

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Saburo Kakei, Tetsuya Kikuchi. 2004-04-15. Affine Lie group approach to a derivative nonlinear Schrödinger equatoin and its similarity reduction. https://arxiv.org/abs/nlin/0403001

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