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

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.