$(2+1)$-Dimensional Local and Nonlocal Reductions of the Negative AKNS System: Soliton Solutions

Abstract

We first construct a $(2+1)$-dimensional negative AKNS hierarchy and then we give all possible local and (discrete) nonlocal reductions of these equations. We find Hirota bilinear forms of the negative AKNS hierarchy and give one- and two-soliton solutions. By using the soliton solutions of the negative AKNS hierarchy we find one-soliton solutions of the local and nonlocal reduced equations.

21 pages

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Cited by in corpus (10)

• Nonlocal KdV Equations
• Discrete Symmetries and Nonlocal Reductions
• Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces
• Nonlocal Hydrodynamic Type of Equations
• Local and nonlocal $(2+1)$-dimensional Maccari systems and their soliton solutions
• Multi-component AKNS systems
• Soliton solutions of the shifted nonlocal NLS and MKdV equations
• Hirota bilinear forms of the AKNS($N$) systems
• $(2+1)$-dimensional AKNS($-N$) Systems: $N=3,4$
• Dbar-approach to coupled nonlocal NLS equation and general nonlocal Reduction