The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure

DOI10.1142/S1402925112500015zbMath1253.37066OpenAlexW2112150643MaRDI QIDQ2883211

Anatoliy K. Prykarpatsky, D. L. Blackmore

Publication date: 11 May 2012

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1402925112500015

zbMATH Keywords

AKNS hierarchyvertex operatorsLax integrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Vertex operators; vertex operator algebras and related structures (17B69) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items

New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties ⋮ The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

Cites Work

• Unnamed Item
• Unnamed Item
• Integrable Hamiltonian systems connected with graded Lie algebras
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Loop groups and equations of KdV type
• Differential-algebraic integrability analysis of the generalized Riemann type and Korteweg–de Vries hydrodynamical equations
• τ functions and zero curvature equations of Toda–AKNS type
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach
• Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
• Functional representation of the Ablowitz-Ladik hierarchy
• Conservation laws for the nonlinear Schr$ouml$dinger equation in Miwa variables
• Functional representations of integrable hierarchies