$(2+1)$-dimensional AKNS($-N$) Systems: $ N=3,4$

TL;DR

This paper extends the study of negative AKNS(N) systems for N=3,4, deriving reductions, bilinear forms, and soliton solutions to deepen understanding of these integrable systems.

Contribution

It provides a comprehensive analysis of negative AKNS(N) systems for N=3,4, including reductions, bilinear forms, and explicit soliton solutions, which were not previously detailed.

Findings

All local and nonlocal reductions obtained.

Hirota bilinear forms constructed.

Explicit one-soliton solutions derived.

Abstract

In this work we continue to study negative AKNS($N$) that is AKNS($-N$) system for $N=3,4$. We obtain all possible local and nonlocal reductions of these equations. We construct the Hirota bilinear forms of these equations and find one-soliton solutions. From the reduction formulas we obtain also one-soliton solutions of all reduced equations.