Snaking and isolas of localised states in bistable discrete lattices

DOI10.1016/j.physleta.2010.10.010zbMath1241.35201arXiv1011.0307OpenAlexW2074466359MaRDI QIDQ430545

Jonathan H. P. Dawes, Chris Taylor

Publication date: 26 June 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0307

zbMATH Keywords

homoclinic snakingcoupled cellsdissipative soliton

Mathematics Subject Classification ID

Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Soliton solutions (35C08) Pattern formations in context of PDEs (35B36) PDEs in connection with statistical mechanics (35Q82)

Related Items (15)

Snakes on Lieb lattice ⋮ Spatially localized structures in lattice dynamical systems ⋮ Localized patterns in planar bistable weakly coupled lattice systems ⋮ Dynamics of waves and patterns. Abstracts from the workshop held August 8--14, 2021 (hybrid meeting) ⋮ Localized Turing patterns in nonlinear optical cavities ⋮ On localised hotspots of an urban crime model ⋮ The Swift-Hohenberg equation with a nonlocal nonlinearity ⋮ Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs ⋮ Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry ⋮ Variational approximations in discrete nonlinear Schrödinger equations with next-nearest-neighbor couplings ⋮ Standing lattice solitons in the discrete NLS equation with saturation ⋮ Isolas of multi-pulse solutions to lattice dynamical systems ⋮ Analysis of cell size effects in atomistic crack propagation ⋮ Snakes in square, honeycomb and triangular lattices ⋮ Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice

Uses Software

• AUTO
• AUTO-07P

Cites Work

• Unnamed Item
• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
• Exponential asymptotics of localised patterns and snaking bifurcation diagrams
• Dissipative solitons.
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Oscillations and patterns in spatially discrete models for developmental intercellular signalling
• Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation
• Patterns and interfaces in dissipative dynamics. With a foreword by Y. Pomeau
• Pattern Formation
• Discrete Snaking: Multiple Cavity Solitons in Saturable Media
• Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
• Two-colour patterns of synchrony in lattice dynamical systems
• Modulated and Localized States in a Finite Domain
• Pattern formation outside of equilibrium
• Patterns of synchrony in lattice dynamical systems

This page was built for publication: Snaking and isolas of localised states in bistable discrete lattices