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

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

1998-11-15

arxiv.org/abs/solv-int/9811010v1

Lett. Math. Phys., 49(2): 95-103, July 1999

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, Revtex, no figures

Scientific paper

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 B\"acklund 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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