A new extended discrete KP hierarchy and generalized dressing method

Details A new extended discrete KP hierarchy and generalized dressing method A new extended discrete KP hierarchy and generalized dressing method

2009-07-16

arxiv.org/abs/0907.2783v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, to appear in J. Phys. A

Scientific paper

Inspired by the squared eigenfunction symmetry constraint, we introduce a new $\ta_k$-flow by ``extending'' a specific $t_n$-flow of discrete KP hierarchy (DKPH). We construct extended discrete KPH (exDKPH), which consists of $t_n$-flow, $\ta_k$-flow and $t_n$ evolution of eigenfunction and adjoin 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.

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