Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice

DOI10.1063/1.4914510zbMath1308.82100OpenAlexW2037055111MaRDI QIDQ5245241

Oleksiy O. Vakhnenko

Publication date: 7 April 2015

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

Full work available at URL: https://doi.org/10.1063/1.4914510

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Statistical mechanics of crystals (82D25) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items (14)

N-fold Darboux transformation of a six-field integrable lattice system ⋮ Asymmetric canonicalization of the integrable nonlinear Schrödinger system on a triangular-lattice ribbon ⋮ Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell ⋮ A hierarchy of integrable differential-difference equations and Darboux transformation ⋮ Positive and negative integrable lattice hierarchies: conservation laws and \(N\)-fold Darboux transformations ⋮ Nonlinear integrable dynamics of coupled vibrational and intra-site excitations on a regular one-dimensional lattice ⋮ Prototype and reduced nonlinear integrable lattice systems with the modulated pulson behavior ⋮ \(N\)-fold Darboux transformations and exact solutions of the combined Toda lattice and relativistic Toda lattice equation ⋮ Soliton elastic interactions and dynamical analysis of a reduced integrable nonlinear Schrödinger system on a triangular-lattice ribbon ⋮ Six-component semi-discrete integrable nonlinear Schrödinger system ⋮ Infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system ⋮ Semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site resonant coupling ⋮ Symmetry-broken canonizations of the semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site coupling ⋮ Four-component integrable systems inspired by the Toda and the Davydov-Kyslukha models

Cites Work

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• New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling
• Darboux transformation of a coupled lattice soliton equation
• A Darboux-Bäcklund transformation associated with a discrete nonlinear Schrödinger equation
• A dressing method in mathematical physics.
• Darboux transformation and the explicit solutions of differential- difference and difference-difference evolution equations. I
• Differential-difference evolution equations. II: Darboux transformation for the Toda lattice
• Quantum difference nonlinear Schrödinger equation
• Physically corrected Ablowitz-Ladik model and its application to the Peierls-Nabarro problem
• Bäcklund transformation for the BC-type Toda lattice
• Darboux transformations in integrable systems. Theory and their applications to geometry
• q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice
• Complete Integrability of General Nonlinear Differential-Difference Equations Solvable by the Inverse Method. II
• Solitons ofq-deformed quantum lattices and the quantum soliton
• Semidiscrete Integrable Nonlinear Systems Generated by the New Fourth-Order Spectral Operator: Local Conservation Laws
• Symplectic methods for the Ablowitz–Ladik discrete nonlinear Schrödinger equation
• On vector analogs of the modified Volterra lattice
• An exact polyhedral model for boron nanotubes
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• Three-component nonlinear dynamical system generated by the new third-order discrete spectral problem
• Solitons in Molecular Systems
• Integrable semi-discretization of the coupled modified KdV equations
• Solitons in parametrically driven discrete nonlinear Schrödinger systems with the exploding range of intersite interactions
• Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry
• Inverse scattering transform for the nonlinear Schrödinger system on a zigzag-runged ladder lattice
• Integrable nonlinear ladder system with background-controlled intersite resonant coupling

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