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Q-Deformed KP Hierarchy: Its Additional Symmetries and Infinitesimal Bäcklund Transformations

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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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  1. Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi, 621, Taiwan

    Ming-Hsien Tu

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  1. Ming-Hsien Tu
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Tu, MH. Q-Deformed KP Hierarchy: Its Additional Symmetries and Infinitesimal Bäcklund Transformations. Letters in Mathematical Physics 49, 95–103 (1999). https://doi.org/10.1023/A:1007647722911

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