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.

arXiv comment30 pages

References in corpus (14)

• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Nonlocal Fordy - Kulish Equations on Symmetric Spaces
• Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
• On integrable wave interactions and Lax pairs on symmetric spaces
• $(2+1)$-Dimensional Local and Nonlocal Reductions of the Negative AKNS System: Soliton Solutions
• Solutions of local and nonlocal equations reduced from the AKNS hierarchy
• On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
• Discrete Symmetries and Nonlocal Reductions
• Nonlocal Coupled HI-MKdV Systems
• Some comments on continuous symmetries of AKNS hierarchy equations and their solutions
• Spectral curves for the rogue waves
• Riemann-Hilbert approach for multi-soliton solutions of a fifth-order nonlinear Schrodinger equation