New integrable \(\mathrm{sl}(2,\mathbb{R})\)-generalization of the classical Wadati-Konno-Ichikawa hierarchy

DOI10.1016/j.cnsns.2014.07.023zbMath1329.37071OpenAlexW2089123789MaRDI QIDQ907696

Haiyan Zhu, Wen-Xiu Ma, Shui Meng Yu, Shou-feng Shen

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.07.023

zbMATH Keywords

symbolic computationHamiltonian structuresoliton hierarchymatrix spectral problemLie algebra \(\mathrm{sl}(2,\mathbb{R})\)

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (4)

Wadati-Konno-Ichikawa-type integrable systems and their constructions ⋮ Three kinds of nonisospectral integrable model of Wadati-Konno-Ichikawa soliton hierarchies ⋮ An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation ⋮ A generalized super AKNS hierarchy associated with Lie superalgebra \(sl(2|1)\) and its super bi-Hamiltonian structure

Uses Software

• Maple
• PDERecursionOperator

Cites Work

• Two hierarchies of multi-component Kaup-Newell equations and theirs integrable couplings
• Multi-component bi-Hamiltonian Dirac integrable equations
• A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order
• A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\)
• Canonical structure of soliton equations. I
• Coupled KdV equations with multi-Hamiltonian structures
• A generalized Wadati--Konno--Ichikawa hierarchy and its binary nonlinearization by symmetry constraints.
• A generalized Wadati-Konno-Ichikawa hierarchy and new finite-dimensional integrable systems
• The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions
• A generalization of the Wadati-Konno-Ichikawa soliton hierarchy and its Liouville integrability
• Adjoint symmetry constraints of multicomponent AKNS equations.
• The multi-component TA hierarchy and its multi-component integrable couplings system with six arbitrary functions
• The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem
• ADJOINT SYMMETRY CONSTRAINTS AND INTEGRABLE COUPLING SYSTEM OF MULTICOMPONENT KN EQUATIONS
• New Integrable Nonlinear Evolution Equations
• An integrable system and associated integrable models as well as Hamiltonian structures
• On Liouville integrability of zero-curvature equations and the Yang hierarchy
• A symbolic algorithm for computing recursion operators of nonlinear partial differential equations
• Coupled Harry Dym equations with multi-Hamiltonian structures
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A trace identity and its application to integrable systems of 1 + 2 dimensions
• An exact solution for a derivative nonlinear Schrödinger equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A coupled AKNS–Kaup–Newell soliton hierarchy
• Lie algebras and Hamiltonian structures of multi-component Ablowitz–Kaup–Newell–Segur hierarchy
• A spectral problem based on so$(3,\mathbb {R})$(3,R) and its associated commuting soliton equations
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• The quadratic-form identity for constructing the Hamiltonian structure of integrable systems
• A trace identity and its applications to the theory of discrete integrable systems
• An integrable counterpart of the D-AKNS soliton hierarchy from \(\mathrm{so}(3,\mathbb R)\)
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: New integrable \(\mathrm{sl}(2,\mathbb{R})\)-generalization of the classical Wadati-Konno-Ichikawa hierarchy