Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls–Nabarro barrier
From MaRDI portal
Publication:3466416
DOI10.1088/0951-7715/29/1/27zbMath1357.37087arXiv1405.3892OpenAlexW2964059687MaRDI QIDQ3466416
Michael J. Jenkinson, Michael I. Weinstein
Publication date: 1 February 2016
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.3892
NLS equations (nonlinear Schrödinger equations) (35Q55) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Partial difference equations (39A14) Growth, boundedness, comparison of solutions to difference equations (39A22)
Related Items
Existence of discrete solitons in discrete nonlinear Schrödinger equations with non-weak couplings ⋮ Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities ⋮ Solutions of the discrete nonlinear Schrödinger equation with a trap ⋮ Breathers as metastable states for the discrete NLS equation ⋮ Ground states in spatially discrete non-linear Schrödinger models ⋮ Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \( h\mathbb{Z}\) ⋮ Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation ⋮ Discrete breathers of nonlinear dimer lattices: bridging the anti-continuous and continuous limits ⋮ Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit ⋮ Existence and Stability of Traveling Waves for Discrete Nonlinear Schrödinger Equations Over Long Times ⋮ Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier ⋮ Nonlinear optical waveguide lattices: asymptotic analysis, solitons, and topological insulators ⋮ On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice
Cites Work
- Unnamed Item
- Traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities
- Homoclinic standing waves in focusing DNLS equations
- On the validity of the variational approximation in discrete nonlinear Schrödinger equations
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
- Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction
- Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential
- The discrete self-trapping equation
- Stability theory of solitary waves in the presence of symmetry. I
- 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
- Existence theorem for solitary waves on lattices
- Decay and analyticity of solitary waves
- Dynamics of lattice kinks
- On asymptotic stability of solitary waves for nonlinear Schrödinger equations
- On the continuum limit for discrete NLS with long-range lattice interactions
- Soliton dynamics in the discrete nonlinear Schrödinger equation
- Stability of waves in discrete systems
- Unimodal wavetrains and solitons in convex Fermi–Pasta–Ulam chains
- The One-Dimensional Case
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- Nonlinear differential–difference equations and Fourier analysis
- Excitation thresholds for nonlinear localized modes on lattices
- Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
- Gap solitons in periodic discrete nonlinear Schrödinger equations
- SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
- Continuous approximation of breathers in one- and two-dimensional DNLS lattices
