Integrable generalizations of the two new soliton hierarchies of AKNS and KN types associated with so(3,ℝ)

2014/06/05 by Chun-Xia Li, Chunxia Li, Shoufeng Shen +9
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 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1406.1326

arxiv created 2014/06/05 · openalex publication_date 2014/06/05 · arxiv updated 2014/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The two matrix spectral problems of Ablowitz-Kaup-Newell-Segur (AKNS) and Kaup-Newell (KN) types associated with so(3,R) are generalized. The corresponding hierarchies of generalized soliton equations are derived by the standard procedure using the zero curvature formulation. Recursion operators and bi-Hamiltonian structures are explicitly constructed for the resulting two generalized soliton hierarchies of AKNS and KN types, which shows their Liouville integrability.

Related

• Two hierarchies of new generalized multicomponent AKNS-type soliton equations
• An integrable generalization of the super Kaup-Newell soliton hierarchy and its bi-Hamiltonian structure
• Vector NLS hierarchy solitons revisited: dressing transformation and tau function approach
• Integrable Hierarchies and Wakimoto Modules
• Non-autonomous soliton hierarchies