Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier

DOI10.1007/s00220-017-2839-4zbMath1397.35276arXiv1601.04598OpenAlexW3100283516MaRDI QIDQ521138

Michael I. Weinstein, Michael J. Jenkinson

Publication date: 6 April 2017

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

Full work available at URL: https://arxiv.org/abs/1601.04598

zbMATH Keywords

bifurcationLyapunov-Schmidt reductiondiscrete nonlinear Schrödinger equationnonlocal interaction

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Bifurcations in context of PDEs (35B32) Soliton solutions (35C08) Fractional partial differential equations (35R11)

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Cites Work

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• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier
• The Pohozaev identity for the fractional Laplacian
• Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
• The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
• Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential
• The discrete self-trapping equation
• The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
• Existence of solitary waves in higher dimensions
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Decay and analyticity of solitary waves
• Dynamics of lattice kinks
• On the continuum limit for discrete NLS with long-range lattice interactions
• Dynamics of partial differential equations
• Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
• Fractional dynamics of systems with long-range interaction
• Algebraic Solitary Waves in Stratified Fluids
• Uniqueness of Radial Solutions for the Fractional Laplacian
• Continuous limit of discrete systems with long-range interaction
• Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls–Nabarro barrier
• Self-similarity in decaying two-dimensional stably stratified adjustment
• Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
• Excitation thresholds for nonlinear localized modes on lattices
• Study of Several Lattice Systems with Long-Range Forces
• A new class of traveling solitons for cubic fractional nonlinear Schrödinger equations
• Blowup for nonlinear wave equations describing boson stars
• Internal waves of permanent form in fluids of great depth
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS