Hirota bilinear forms of the AKNS(N) systems

2020/01/30 by Metin Gürses, Gürses, Metin, Aslı Pekcan +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2001.11391

openalex publication_date 2020/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Some comments on continuous symmetries of AKNS hierarchy equations and their solutions
• Integrable Nonlocal Nonlinear Equations
• Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions
• Riemann-Hilbert approach for multi-soliton solutions of a fifth-order nonlinear Schrodinger equation

Related

• (2+1)-dimensional AKNS(-N) Systems: N=3,4
• Multilinear Hirota operators and integrability
• Stationary systems of the AKNS hierarchy
• Some comments on continuous symmetries of AKNS hierarchy equations and their solutions
• Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy