2008/10/10 by Runliang Lin, Xiaojun Liu, Yunbo Zeng · 1 citation
Physics and Astronomy · #nlin.SI
paper · pdf · doi:10.2991/jnmp.2008.15.3.6
17 pages, no figure
arxiv created 2008/10/10 · arxiv updated 2015/05/12
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-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 q 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.