$(2+1)$-Dimensional Local and Nonlocal Reductions of the Negative AKNS System: Soliton Solutions

TL;DR

This paper develops a $(2+1)$-dimensional negative AKNS hierarchy, explores its local and nonlocal reductions, and derives soliton solutions, including explicit one- and two-soliton solutions for the reduced equations.

Contribution

It introduces a comprehensive framework for the negative AKNS hierarchy with all possible reductions and explicit soliton solutions, expanding understanding of integrable systems.

Findings

Constructed the $(2+1)$-dimensional negative AKNS hierarchy.

Derived Hirota bilinear forms and soliton solutions.

Obtained explicit soliton solutions for reduced equations.

Abstract

We first construct a $(2+1)$-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.