Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure

DOI10.1063/1.529205zbMath0736.35124OpenAlexW2012722986MaRDI QIDQ3980919

Hong-Wei Zhang, Walter Oevel, Benno Fuchssteiner, Gue-Zhang Tu

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529205

zbMATH Keywords

symmetriesrecursion operatorsconserved quantitiesLax pairmastersymmetriesnonlinear lattice systems

Mathematics Subject Classification ID

Related Items (67)

INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ Tri-Hamiltonian duality system of Merola-Ragnisco-Tu equation ⋮ Finite genus solutions of the generalized Merola–Ragnisco–Tu lattice hierarchy ⋮ Nonlinear discrete systems with nonanalytic dispersion relations ⋮ Integrable discretizations of the Bogoyavlensky lattices ⋮ A direct algorithm for constructing recursion operators and Lax pairs for integrable models ⋮ Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A^{(1)}_{N-1}$ ⋮ Integrable nonlinear evolution equations with time-dependent coefficients ⋮ Analytical Bethe ansatz, canonical Bäcklund transformation and \(Q\)-operator for a new discrete integrable hierarchy ⋮ A family of integrable differential-difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs ⋮ The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices ⋮ Algorithmic determination of infinite-dimensional symmetry groups for integrable systems in \(1+1\) dimensions ⋮ Discrete Painlevé equations: coalescences, limits and degeneracies ⋮ Discrete moving frames and discrete integrable systems ⋮ Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants ⋮ Inverse spectral transform for the Ragnisco-Tu equation with heaviside initial condition ⋮ Rational Solutions of an Extended Lotka-Volterra Equation ⋮ Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. II. The reduction via Dirac and canonical quantization procedure ⋮ Integrable lattice hierarchies associated with two new (2+1)-dimensional discrete spectral problems ⋮ Hungry Lotka–Volterra lattice under nonzero boundaries, block‐Hankel determinant solution, and biorthogonal polynomials ⋮ Bogoyavlensky lattices and generalized Catalan numbers ⋮ Riemann-Hilbert problems and soliton solutions for a generalized coupled Sasa-Satsuma equation ⋮ Dynamics of higher‐order rational and semi‐rational soliton solutions of the coupled modified KdV lattice equation ⋮ On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators ⋮ Classification of five-point differential–difference equations II ⋮ On classification of discrete, scalar-valued Poisson brackets ⋮ Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem ⋮ A lattice hierarchy and its continuous limits ⋮ A Liouville integrable lattice soliton equation, infinitely many conservation laws and integrable coupling systems ⋮ New integrable lattice hierarchies ⋮ A 2-PARAMETER HIERARCHY OF INTEGRABLE LATTICE EQUATIONS ⋮ Nonlinear integrable systems containing the canonical subsystems of distinct physical origins ⋮ Classification of five-point differential-difference equations ⋮ Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure ⋮ Two-component generalized Ragnisco-Tu equation and the Riemann-Hilbert problem ⋮ Darboux transformations and recursion operators for differential-difference equations ⋮ Lax pairs, symmetries and conservation laws of a differential-difference equation -- Sato's approach ⋮ Algebro-geometric solutions of the discrete Ragnisco-Tu hierarchy ⋮ A higher-dimensional Lie algebra and its decomposed subalgebras ⋮ Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice ⋮ \(N\)-fold Darboux transformation and solitonic interactions for a Volterra lattice system ⋮ A hierarchy of discrete Hamiltonian equations and its binary nonlinearization by symmetry constraint ⋮ New hierarchies of integrable positive and negative lattice models and Darboux transformation ⋮ The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters ⋮ Positive and negative hierarchies of nonlinear integrable lattice models and three integrable coupling systems associated with a discrete spectral problem ⋮ The exact solutions to a Ragnisco-Tu hierarchy with self-consistent sources ⋮ Factorization of a hierarchy of the lattice soliton equations from a binary Bargmann symmetry constraint ⋮ THE INTEGRABLE PROPERTY OF LOTKA–VOLTERRA TYPE DISCRETE NONLINEAR LATTICE SOLITON SYSTEMS ⋮ An unusual series of autonomous discrete integrable equations on a square lattice ⋮ Discrete time Toda systems ⋮ Solving an integrable coupling system of Merola-Ragnisco-Tu lattice equation by Darboux transformation of Lax pair ⋮ Explicit solutions of the coupled Bogoyavlensky lattice 1(2) Hierarchy ⋮ Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations ⋮ A lattice hierarchy with a free function and its reductions to the Ablowitz-Ladik and Volterra hierarchies ⋮ Bi-Hamiltonian structure of modified Volterra model ⋮ Symmetry Constraint of the Differential-difference KP Hierarchy and a Second Discretization of the ZS-AKNS System ⋮ An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family ⋮ Positive and negative integrable hierarchies, associated conservation laws and Darboux transformation ⋮ Singularity structure and algebraic properties of the differential-difference Kadomtsev-Petviashvili equation. ⋮ Rational recursion operators for integrable differential-difference equations ⋮ Four-component integrable systems inspired by the Toda and the Davydov-Kyslukha models ⋮ Integrable modifications of the Ito-Narita-Bogoyavlensky equation ⋮ On the recursion operators for integrable equations ⋮ Restricted flows of a hierarchy of integrable discrete systems ⋮ A family of Liouville integrable lattice equations with a parameter and its two symmetry constraints ⋮ Three-sheeted Riemann surface and solutions of the Itoh–Narita–Bogoyavlensky lattice hierarchy ⋮ A Bäcklund transformation and nonlinear superposition formula for the Lotka-Volterra hierarchy

Cites Work

• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• On a new hierarchy of symmetries for the Kadomtsev-Petviashvili equation
• Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows
• Soliton-like behavior in automata
• Self-adjointness of elliptic operators with infinitely many variables
• Classical and quantum-mechanical systems of Toda lattice type. I
• Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems
• The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• Interaction of Simple Particles in Soliton Cellular Automata
• Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice
• Application of hereditary symmetries to nonlinear evolution equations
• Bäcklund transformations for hereditary symmetries
• Nonlinear differential–difference equations and Fourier analysis
• Evolution equations possessing infinitely many symmetries
• Evolution Theory, Periodic Particles, and Solitons in Cellular Automata
• Experimental mathematics

This page was built for publication: Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure