A new extended discrete KP hierarchy and a generalized dressing method

Abstract

Inspired by the squared eigenfunction symmetry constraint, we introduce a new τk-flow by ‘extending’ a specific tn-flow of a discrete KP hierarchy (DKPH). We construct an extended discrete KPH (exDKPH), which consists of tn-flow, τk-flow and tn evolution of eigenfunction and adjoint eigenfunctions, and its Lax representation. The exDKPH contains two types of discrete KP equation with self-consistent sources (DKPESCS). Two reductions of exDKPH are obtained. The generalized dressing approach for solving the exDKPH is proposed and the N-soliton solutions of two types of the DKPESCS are presented.