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Q-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformations

Ming-Hsien Tu
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Abstract

We study the additional symmetries associated with the $q$-deformed Kadomtsev-Petviashvili ($q$-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the $q$-KP hierarchy can be consistently reduced to the so-called $q$-deformed constrained KP ($q$-cKP) hierarchy. We then show that the additional symmetries acting on the wave function can be viewed as infinitesimal Bäcklund transformations by acting the vertex operator on the tau-function of the $q$-KP hierarchy. This establishes the Adler-Shiota-van Moerbeke formula for the $q$-KP hierarchy.

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Ming-Hsien Tu. 1998-11-15. Q-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformations. https://arxiv.org/abs/solv-int/9811010

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