Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy

TL;DR

This paper introduces new (2+1)-dimensional integrable hierarchies extending the KP framework, incorporating self-consistent sources, and employs Darboux transformations to generate solutions, broadening the understanding of integrable systems.

Contribution

It proposes novel extensions of KP hierarchies with self-consistent sources and applies Darboux transformations to find solutions, advancing integrable systems theory.

Findings

New (2+1)-dimensional integrable equations including DS-III and N-wave problem.

Recovery of a system with two types of KP equations as special cases.

Application of Darboux transformations to generate explicit solutions.

Abstract

New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem. Furthermore, we recover a system that contains two types of the KP equation with self-consistent sources as special cases. Darboux and binary Darboux transformations are applied to generate solutions of the proposed hierarchies.