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

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.