Hirota bilinear forms of the AKNS($N$) systems

TL;DR

This paper derives Hirota bilinear forms for the AKNS(N) hierarchy for N=3 to 6, explores their reductions, and studies the compatibility of various transformations and reductions.

Contribution

It provides explicit Hirota bilinear forms for higher-order AKNS(N) systems and analyzes their reductions and compatibility with recursion operators.

Findings

Hirota bilinear forms for AKNS(3) to AKNS(6) systems are established.

Local and nonlocal reductions of these systems are presented.

Compatibility between recursion operators, reductions, and Hirota bilinearization is demonstrated.

Abstract

We study the AKNS($N$) hierarchy for $N=3,4,5,6$. We give the Hirota bilinear forms of these systems and present local and nonlocal reductions of them. We give the Hirota bilinear forms of the reduced equations. The compatibility of the commutativity diagrams of the application of the recursion operator, reductions of the AKNS($N$) systems, and Hirota bilinearization is also studied.