Differential-difference Kadomtsev-Petviashvili equation: properties and integrability

Abstract

We present a review on certain integrability properties of dlfferencial-dlfference Kadomtsev-Petviashvih (DAKP) equation. We explain the dlfferential-dlfference version of Sala theory and derive the DAKP equation as a first nontrivial member in the single- component KP family. In the process, we exploit the Sato theory to obtain conservation law, and generalised symmetries of the same. We further show that the Wronskian form of the N-solution solutions and follow naturally from this approach Similiarly reduction and Paintive-singularity confinement analysis are performed. We also discuss a gauge eqvivalence of the DAKP equation and study certain integrability properties of interesting system as well.