The Ablowitz-Ladik system on a graph

DOI10.1088/1361-6544/ab36f2zbMath1427.37058arXiv1903.09040OpenAlexW2924972060MaRDI QIDQ5240863

Baoqiang Xia

Publication date: 29 October 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.09040

zbMATH Keywords

initial-boundary value probleminverse scattering methodAblowitz-Ladik systemunified transform method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lattice dynamics; integrable lattice equations (37K60)

Cites Work

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• Threshold phenomena and existence results for NLS ground states on metric graphs
• Affine Toda field theories with defects
• Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs
• Constrained energy minimization and orbital stability for the NLS equation on a star graph
• The Degasperis-Procesi equation on the half-line
• Surface solitons in trilete lattices
• Variational properties and orbital stability of standing waves for NLS equation on a star graph
• The reduction problem and the inverse scattering method
• Initial-boundary value problems associated with the Ablowitz-Ladik system
• A multisymplectic approach to defects in integrable classical field theory
• Integrable nonlinear evolution equations on the half-line
• Quantum spins on star graphs and the Kondo model
• Boundary conditions for integrable chains
• New integrable boundary conditions for the Ablowitz-Ladik model: from Hamiltonian formalism to nonlinear mirror image method
• On the inverse scattering method for integrable PDEs on a star graph
• Integrable nonlinear evolution equations on a finite interval
• Soliton propagation on chains with simple nonlocal defects
• Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval
• Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• The unified transform method for the Sasa–Satsuma equation on the half-line
• The unified method: I. Nonlinearizable problems on the half-line
• Nonlinear Schrödinger equation on graphs: recent results and open problems
• FAST SOLITONS ON STAR GRAPHS
• The Ablowitz–Ladik system on a finite set of integers
• CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS
• The Ablowitz–Ladik system with linearizable boundary conditions
• A Unified Approach to Boundary Value Problems
• Initial-boundary-value problems for discrete evolution equations: discrete linear Schrödinger and integrable discrete nonlinear Schrödinger equations
• The Ablowitz-Ladik system on the natural numbers with certain linearizable boundary conditions
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• Kirchhoff's rule for quantum wires
• A unified transform method for solving linear and certain nonlinear PDEs
• Integrable Nonlocal Nonlinear Equations
• Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
• The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs
• Aspects of sine-Gordon solitons, defects and gates
• Boundary value problems for integrable equations compatible with the symmetry algebra
• Finite genus solutions to the Ablowitz‐Ladik equations
• The nonlinear Schrödinger equation on the half-line
• Jump-defects in the nonlinear Schrödinger model and other non-relativistic field theories
• ON A SYSTEMATIC APPROACH TO DEFECTS IN CLASSICAL INTEGRABLE FIELD THEORIES

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