(2+1)-dimensional AKNS(-N) systems II

In our previous work (Gurses and Pekcan, 2019, [40]) we started to investigate negative AKNS(-N) hierarchy in (2 + 1)-dimensions. We were able to obtain only the first three, N = 0, 1, 2, members of this hierarchy. The main difficulty was the nonexistence of the Hirota formulation of the AKNS(N) hierarchy for N >= 3. Here in this work we overcome this difficulty for N = 3, 4 and obtain Hirota bilinear forms of (2 + 1)-dimensional AKNS(-N) equations for these members. We study the local and nonlocal reductions of these systems of equations and obtain several new integrable local and nonlocal equations in (2 + 1)-dimensions. We also give one-, two-, and three-soliton solutions of the reduced equations. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study addressed the challenge of the nonexistence of Hirota formulation for AKNS(N) hierarchy for N >= 3 in (2 + 1) dimensions. The researchers overcame this difficulty for N = 3, 4 and obtained Hirota bilinear forms for these members. They explored local and nonlocal reductions of the equations and derived new integrable equations in (2 + 1) dimensions.