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

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2021-06

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Abstract

In our previous work (Gürses 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

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Communications in Nonlinear Science and Numerical Simulation

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Elsevier BV

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Ablowitz-Musslimani type of reductions, (2 + 1)-dimensional negative AKNS systems, Hirota method, Soliton solutions

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Published Version (Please cite this version)

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English

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Article