A new extended q-deformed KP hierarchy
Exactly Solvable and Integrable Systems
2015-05-13 v1
Abstract
A method is proposed in this paper to construct a new extended q-deformed KP (-KP) hiearchy and its Lax representation. This new extended -KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations.
Cite
@article{arxiv.0810.1862,
title = {A new extended q-deformed KP hierarchy},
author = {Runliang Lin and Xiaojun Liu and Yunbo Zeng},
journal= {arXiv preprint arXiv:0810.1862},
year = {2015}
}
Comments
17 pages, no figure