Multi-component AKNS systems

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. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

We study two members of the multi-component AKNS hierarchy, namely the multi-NLS and multi-MKdV systems. The Hirota bilinear forms of these equations are derived, and soliton solutions are obtained. All possible local and nonlocal reductions of these systems of equations are found, and a prescription is given to obtain their soliton solutions. (2 + 1)-dimensional extensions of the multi-component AKNS systems are also derived.