DIS

Abstract

We extend the discrete KP hierarchy (DKPH) by its symmetry restriction. This extended DKPH (exDKPH) includes the discrete KP equation with self-consistent sources (DKPESCS) as its first nontrivial equation. Lax representation of exDKPH is also pressented. The DKPESCS can be considered to be DKPE with non-homogeneous terms. By directly applying the method of variation of constant to the solutions of the DKPE obtained by Darboux transformation and its corresponding eigenfunctions, we construct the solutions of the DKPESCS.