A new extended q-deformed KP hierarchy

Abstract

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.

17 pages, no figure

References in corpus (2)

• A new extended KP hierarchy
• R-matrix approach to integrable systems on time scales

Cited by in corpus (6)

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• A new $({\gamma }_n,{\sigma }_k)-$ KP hierarchy and generalized dressing method
• The generalised q-Wronskian solutions of the q-deformed constrained modified KP hierarchy