Q-deformed KP hierarchy: Its additional symmetries and infinitesimal B\"acklund transformations
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
We study the additional symmetries associated with the -deformed Kadomtsev-Petviashvili (-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the -KP hierarchy can be consistently reduced to the so-called -deformed constrained KP (-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 -KP hierarchy. This establishes the Adler-Shiota-van Moerbeke formula for the -KP hierarchy.
Keywords
Cite
@article{arxiv.solv-int/9811010,
title = {Q-deformed KP hierarchy: Its additional symmetries and infinitesimal B\"acklund transformations},
author = {Ming-Hsien Tu},
journal= {arXiv preprint arXiv:solv-int/9811010},
year = {2007}
}
Comments
9 pages, Revtex, no figures