Multi-component AKNS systems

TL;DR

This paper investigates multi-component AKNS systems, deriving Hirota bilinear forms, soliton solutions, and reductions, including nonlocal and higher-dimensional extensions, advancing the understanding of integrable multi-component nonlinear equations.

Contribution

It introduces new multi-component AKNS systems, derives their Hirota forms, soliton solutions, and explores local/nonlocal reductions and higher-dimensional extensions.

Findings

Derived Hirota bilinear forms for multi-component AKNS systems

Obtained explicit soliton solutions for these systems

Identified all possible local and nonlocal reductions

Abstract

We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton solutions. We find all possible local and nonlocal reductions of these systems of equations and give a prescription to obtain their soliton solutions. We derive also $(2+1)$-dimensional extensions of the multi-component AKNS systems.