Continuous limit of discrete systems with long-range interaction
From MaRDI portal
Publication:3421678
DOI10.1088/0305-4470/39/48/005zbMath1197.82044arXiv0711.0826OpenAlexW3105823702MaRDI QIDQ3421678
Publication date: 8 February 2007
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0711.0826
Boussinesq equationBurgers equationKorteweg-de Vries equationlong-range interactionRiesz fractional derivativepower-law interactionfractional lattice equations
Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Lattice dynamics; integrable lattice equations (37K60)
Related Items
On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme, Lattice fractional calculus, A numerically efficient dissipation-preserving implicit method for a nonlinear multidimensional fractional wave equation, United lattice fractional integro-differentiation, Fractional derivative regularization in QFT, Fractional-order difference equations for physical lattices and some applications, A stable numerical method for space fractional Landau-Lifshitz equations, Equilibrium time-correlation functions of the long-range interacting Fermi–Pasta–Ulam model, A fully explicit variational integrator for multidimensional systems of coupled nonlinear fractional hyperbolic equations, Partial fractional derivatives of Riesz type and nonlinear fractional differential equations, A fractional generalization of the classical lattice dynamics approach, Biquaternionic reformulation of a fractional monochromatic Maxwell system, Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation, A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives, An easy-to-implement parallel algorithm to simulate complex instabilities in three-dimensional (fractional) hyperbolic systems, A stable and convergent finite-difference model which conserves the positivity and the dissipativity of Gibbs' free energy for a nonlinear combustion equation, Nonlinear supratransmission in fractional wave systems, On the continuum limit for discrete NLS with long-range lattice interactions, Exact discretization of Schrödinger equation, Temporal monotonicity of the solutions of some semilinear parabolic equations with fractional diffusion, On the solution of hyperbolic two-dimensional fractional systems via discrete variational schemes of high order of accuracy, Exact discretization by Fourier transforms, Onto resolving spurious wave reflection problem with changing nonlocality among various length scales, An energy-preserving and efficient scheme for a double-fractional conservative Klein-Gordon-Zakharov system, Numerical simulation of the nonlinear dynamics of harmonically driven Riesz-fractional extensions of the Fermi-Pasta-Ulam chains, Fractional calculus of variations in terms of a generalized fractional integral with applications to physics, An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions, Supratransmission in \(\beta\)-Fermi-Pasta-Ulam chains with different ranges of interactions, Fractional generalization of the Fermi-Pasta-Ulam-Tsingou media and theoretical analysis of an explicit variational scheme, A numerically efficient variational algorithm to solve a fractional nonlinear elastic string equation, On the analyticity for the generalized quadratic derivative complex Ginzburg-Landau equation, Algorithm for some anomalously diffusive hyperbolic systems in molecular dynamics: theoretical analysis and pattern formation, A parallelized computational model for multidimensional systems of coupled nonlinear fractional hyperbolic equations, On the dissipativity of some Caputo time-fractional subdiffusion models in multiple dimensions: theoretical and numerical investigations, Integrable coupling system of fractional soliton equation hierarchy, Large lattice fractional Fokker–Planck equation, A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics, Wave transmission and reflection analysis through complex media based on the second strain gradient theory, Fractional vector calculus and fractional Maxwell's equations, Stochastic scattering model of anomalous diffusion in arrays of steady vortices, Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier, A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains, Fractional Schrödinger dynamics and decoherence, An efficient Hamiltonian numerical model for a fractional Klein-Gordon equation through weighted-shifted Grünwald differences, A bounded and efficient scheme for multidimensional problems with anomalous convection and diffusion, Nonlocal elasticity: an approach based on fractional calculus, Fractional Liouville equation on lattice phase-space, On a nonlinear energy-conserving scalar auxiliary variable (SAV) model for Riesz space-fractional hyperbolic equations, Hidden Coexisting Attractors in a Chaotic System Without Equilibrium Point, An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy, A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross-Pitaevskii equation, Non-linear fractional field equations: weak non-linearity at power-law non-locality, Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials, Design and analysis of a dissipative scheme to solve a generalized multi-dimensional Higgs boson equation in the de Sitter space-time, Theoretical analysis of a conservative finite-difference scheme to solve a Riesz space-fractional Gross-Pitaevskii system, Fractional standard map, Chaotic vibration in fractional maps, Nonlocal quantum system with fractal distribution of states, Two energy-preserving numerical models for a multi-fractional extension of the Klein-Gordon-Zakharov system, REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS, On the solution of a generalized Higgs boson equation in the de Sitter space-time through an efficient and Hamiltonian scheme, A numerically efficient Hamiltonian method for fractional wave equations, Exact discrete analogs of derivatives of integer orders: differences as infinite series, Fractional quantum field theory: from lattice to continuum, Numerical Simulations in Nonlinear Elastic Metamaterials with Nonlocal Interaction, On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice, Fractional dynamics and modulational instability in long-range Heisenberg chains, Nonlocal statistical mechanics: general fractional Liouville equations and their solutions, On a New Class of Variational Problems, Energy transmission in the forbidden band-gap of a nonlinear chain with global interactions, Discrete monotone method for space-fractional nonlinear reaction-diffusion equations, Three-dimensional lattice models with long-range interactions of Grünwald-Letnikov type for fractional generalization of gradient elasticity
