DOI10.1088/0305-4470/23/17/020zbMath0717.58027OpenAlexW2045487127MaRDI QIDQ5748617
Gue-Zhang Tu
Publication date: 1990
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0305-4470/23/17/020
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Ergodic theorems, spectral theory, Markov operators (37A30)
Integrability, multi-soliton and rational solutions, and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter ⋮
Wadati-Konno-Ichikawa-type integrable systems and their constructions ⋮
A generalized integrable lattice hierarchy related to the Ablowitz–Ladik lattice: Conservation law, Darboux transformation and exact solution ⋮
Some soliton hierarchies associated with Lie algebras \(\mathfrak{sp}(4)\) and \(\mathfrak{so}(5)\) ⋮
A discrete KdV equation hierarchy: continuous limit, diverse exact solutions and their asymptotic state analysis ⋮
A novel kind of a multicomponent hierarchy of discrete soliton equations and its application ⋮
The relationship between the conservation laws and multi‐Hamiltonian structures of the Kundu equation ⋮
Dynamics of higher‐order rational and semi‐rational soliton solutions of the coupled modified KdV lattice equation ⋮
Liouville integrability and explicit solutions for a Frobenius‐coupled integrable lattice hierarchy ⋮
Lie algebras and Hamiltonian structures of multi-component Ablowitz–Kaup–Newell–Segur hierarchy ⋮
Hierarchy of lax integrable lattice equations, darboux transformation and conservation laws ⋮
A generalized Ablowitz–Ladik hierarchy, multi-Hamiltonian structure and Darboux transformation ⋮
Generalized integrable hierarchies of AKNS type, super Dirac type and super NLS-mKdV type ⋮
Generating integrable lattice hierarchies by some matrix and operator Lie algebras ⋮
Two kinds of discrete integrable hierarchies of evolution equations and some algebraic-geometric solutions ⋮
Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources ⋮
The application of discrete variational identity on semi-direct sums of Lie algebras ⋮
A super-soliton hierarchy and its super-Hamiltonian structure ⋮
Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques ⋮
A vector generalization of Volterra type differential-difference equations ⋮
An integrable lattice hierarchy based on suris system: \(N\)-fold Darboux transformation and conservation laws ⋮
Lax representations and zero-curvature representations by the Kronecker product ⋮
An Ablowitz-Ladik integrable lattice hierarchy with multiple potentials ⋮
Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling ⋮
New lattice equation hierarchies and Darboux transformation ⋮
Nonlinearization of the Lax pairs for discrete Ablowitz-Ladik hierarchy. ⋮
A family of integrable differential-difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs ⋮
A hierarchy of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformations ⋮
A new integrable lattice hierarchy associated with a discrete \(3\times 3\) matrix spectral problem: \(N\)-fold Darboux transformation and explicit solutions ⋮
Analytical insights into a generalized semidiscrete system with time-varying coefficients: derivation, exact solutions, and nonlinear soliton dynamics ⋮
An integrable lattice hierarchy associated with a \(4 \times 4\) matrix spectral problem: \(N\)-fold Darboux transformation and dynamical properties ⋮
A family of Liouville integrable lattice equations and its conservation laws ⋮
A new hierarchy of integrable system of \(1+2\) dimensions: from Newton's law to generalized Hamiltonian system. II. ⋮
Constructing nonlinear discrete integrable Hamiltonian couplings ⋮
New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling ⋮
Periodic waves in the discrete mKdV equation: modulational instability and rogue waves ⋮
A hierarchy of integrable differential-difference equations and Darboux transformation ⋮
A New Integrable Symplectic Map of Neumann Type ⋮
New soliton hierarchies associated with the real Lie algebra so(4,R) ⋮
R-matrix approach to lattice integrable systems ⋮
Variational identities and applications to Hamiltonian structures of soliton equations ⋮
A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation ⋮
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation ⋮
An integrable lattice hierarchy, associated integrable coupling, Darboux transformation and conservation laws ⋮
Initial-boundary value problems associated with the Ablowitz-Ladik system ⋮
New integrable \(\mathrm{sl}(2,\mathbb{R})\)-generalization of the classical Wadati-Konno-Ichikawa hierarchy ⋮
A New Negative Discrete Hierarchy and ItsN-Fold Darboux Transformation ⋮
N-fold Darboux transformation and soliton solutions for Toda lattice equation ⋮
Nonlinear integrable systems containing the canonical subsystems of distinct physical origins ⋮
Dynamics of bright and dark multi-soliton solutions for two higher-order Toda lattice equations for nonlinear waves ⋮
\(N\)-fold Darboux transformation of the discrete Ragnisco-Tu system ⋮
Positive and negative integrable lattice hierarchies: conservation laws and \(N\)-fold Darboux transformations ⋮
Positive and negative integrable hierarchies: bi-Hamiltonian structure and Darboux-Bäcklund transformation ⋮
Conservation laws and self-consistent sources for an integrable lattice hierarchy associated with a three-by-three discrete matrix spectral problem ⋮
A hierarchy of new discrete integrable equation and its Hamiltonian structure ⋮
A family of integrable different-difference equations, its Hamiltonian structure, and Darboux-Bäcklund transformation ⋮
The relation between the Toda hierarchy and the KdV hierarchy ⋮
Integrable coupling of the Ablowitz-Ladik hierarchy and its Hamiltonian structure ⋮
Coupled discrete Sawada-Kotera equations and their explicit quasi-periodic solutions ⋮
A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems ⋮
The bi-integrable couplings of two-component Casimir-Qiao-Liu type hierarchy and their Hamiltonian structures ⋮
A generalized integrable lattice hierarchy associated with the Toda and modified Toda lattice equations: Hamiltonian representation, soliton solutions ⋮
\(N\)-fold Darboux transformation and solitonic interactions for a Volterra lattice system ⋮
An algebro-geometric solution for a Hamiltonian system with application to dispersive long wave equation ⋮
Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows ⋮
A generating scheme for conservation laws of discrete zero curvature equations and its application ⋮
Super Jaulent-Miodek hierarchy and its super Hamiltonian structure, conservation laws and its self-consistent sources ⋮
New hierarchies of integrable positive and negative lattice models and Darboux transformation ⋮
An integrable \(\text{SO}(3,\mathbb{R})\)-counterpart of the Heisenberg soliton hierarchy ⋮
The integrable coupling system of a \(3 \times 3\) discrete matrix spectral problem ⋮
Two families of Liouville integrable lattice equations ⋮
Semi-direct sums of Lie algebras and continuous integrable couplings ⋮
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 ⋮
Hamiltonian structure and infinite number of conservation laws for the coupled discrete KdV equations ⋮
A new multi-component discrete integrable hierarchy and multi-component cubic Volterra integrable hierarchy as well as their coupling systems ⋮
New integrable lattice hierarchies and associated properties ⋮
A discrete iso-spectral problem with positive and negative hierarchies and integrable coupling system ⋮
New form \((2+1)\)-dimensional integrable lattice hierarchies with two shift operators Ẽ and Ê ⋮
Factorization of a hierarchy of the lattice soliton equations from a binary Bargmann symmetry constraint ⋮
The Darboux transformation associated with two-parameter lattice soliton equation ⋮
The Liouville integrability of integrable couplings of Volterra lattice equation ⋮
Two super-integrable hierarchies and their super-Hamiltonian structures ⋮
A new non-isospectral integrable couplings for generalized Volterra lattice hierarchy ⋮
Two \(3 \times 3\) discrete matrix spectral problems and associated Liouville integrable lattice soliton equations ⋮
Component-trace identity for Hamiltonian structure of the integrable couplings of the giachetti-johnson (GJ) hierarchy and coupling integrable couplings ⋮
Construction of solutions for an integrable differential-difference equation by Darboux-Bäcklund transformation ⋮
Solving an integrable coupling system of Merola-Ragnisco-Tu lattice equation by Darboux transformation of Lax pair ⋮
Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures ⋮
Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures ⋮
A Darboux transformation for the Volterra lattice equation ⋮
New super integrable hierarchies associated with \(\operatorname{osp}(2|2)\) and \(\operatorname{spo}(2|2)\) and their applications ⋮
A non-isospectral integrable couplings of Volterra lattice hierarchy with self-consistent sources ⋮
Constructing integrable coupling systems of Hamiltonian lattice equations using semi-direct sums of Lie algebras ⋮
Algebro-geometric solutions for some \((2+1)\)-dimensional discrete systems ⋮
Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations ⋮
Notes on ``A integrable lattice hierarchy based on Suris system: N-fold Darboux transformation and conservation laws ⋮ A lattice hierarchy with a free function and its reductions to the Ablowitz-Ladik and Volterra hierarchies ⋮ A new lattice hierarchy: Hamiltonian structures, symplectic map and \(N\)-fold Darboux transformation ⋮ A family of integrable differential-difference equations: tri-Hamiltonian structure and Lie algebra of vector fields
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