Existence theorem for solitary waves on lattices

From MaRDI portal
Publication:1325591

DOI10.1007/BF02099784zbMath0807.35121MaRDI QIDQ1325591

Gero Friesecke, Jonathan A. D. Wattis

Publication date: 9 March 1995

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




Related Items (99)

Breathers in a locally resonant granular chain with precompressionTravelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-toriNONLINEAR WAVES IN NEWTON'S CRADLE AND THE DISCRETE p-SCHRÖDINGER EQUATIONUnstable dynamics of solitary traveling waves in a lattice with long-range interactionsTravelling breathers in Klein-Gordon chainsMicropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limitGround states for infinite lattices with nearest neighbor interactionCnoidal waves on Fermi-Pasta-Ulam latticesOSCILLATORY WAVES IN DISCRETE SCALAR CONSERVATION LAWSBreathers on diatomic Fermi-Pasta-Ulam latticesPeriodic and solitary travelling waves in infinite lattices without Ambrosetti-Rabinowitz conditionAnalysis, simulation and visualization of 1D tapping via reduced dynamical modelsSolitary waves in FPU-type latticesAsymptotic stability of lattice solitons in the energy spaceTraveling waves for the mass in mass model of granular chainsExistence of periodic traveling waves in Fermi-Pasta-Ulam type systems on 2D-lattice with saturable nonlinearitiesOnsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls–Nabarro barrierAn energy-based stability criterion for solitary travelling waves in Hamiltonian latticesTravelling breathers and solitary waves in strongly nonlinear latticesUnnamed ItemKdV-like solitary waves in two-dimensional FPU-latticesSolitary waves with prescribed speed on infinite latticesSmall planar travelling waves in two-dimensional networks of coupled oscillatorsExistence of traveling waves for a class of nonlocal nonlinear equations with Bell shaped kernelsSmall mass nanopteron traveling waves in mass-in-mass lattices with cubic FPUT potentialPeriodic traveling waves in diatomic granular chainsOn the evolution of scattering data under perturbations of the Toda latticePeriodic travelling waves and compactons in granular chainsExistence and multiplicity of wave trains in a 2D diatomic face-centered latticeMass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripplesNecessary conditions for breathers on continuous media to approximate breathers on discrete latticesNanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratioExponential asymptotics of woodpile chain nanoptera using numerical analytic continuationPeriodic traveling wave solutions of discrete nonlinear Klein‐Gordon latticesTraveling wave solutions for the FPU chain: a constructive approachNanopteron-stegoton traveling waves in spring dimer Fermi-Pasta-Ulam-Tsingou latticesMoving Modulating Pulse and Front Solutions of Permanent Form in a FPU Model with Nearest and Next-to-Nearest Neighbor InteractionPrimary wave transmission in the hexagonally packed, damped granular crystal with a spatially varying cross sectionAsymptotic stability of \(N\)-solitary waves of the FPU latticesPeriodic and homoclinic travelling waves in infinite latticesAction minimising fronts in general FPU-type chainsWave propagation in a strongly nonlinear locally resonant granular crystalCombined breathing-kink modes in the FPU latticeExistence of traveling solitary waves in Fermi-Pasta-Ulam-type systems with saturable nonlinearities on 2D-latticeMultiple periodic solutions for lattice dynamical systems with superquadratic potentialsA new barrier to the existence of moving kinks in Frenkel-Kontorova latticesCenter Manifold Theory in the Context of Infinite One-Dimensional LatticesUniform sliding states in the undamped Frenkel-Kontorova modelStrictly supersonic solitary waves in lattices with second-neighbor interactionsExistence criterion of solitary waves in a chain of grainsNanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equationExistence and multiplicity of wave trains in 2D latticesTravelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potentialModulation of solitary waves and formation of stable attractors in granular scalar models subjected to on-site perturbationPeriodic motion for FPU lattice dynamical systems with the strongly indefinite caseJustification of leading order quasicontinuum approximations of strongly nonlinear latticesModulation of uniform motion in diatomic Frenkel-Kontorova modelCompacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granulesNontrivial periodic motions for resonant type asymptotically linear lattice dynamical systemsNonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limitsLocalized waves in nonlinear oscillator chainsPeriodic travelling wave solutions of discrete nonlinear Schrödinger equationsPeriodic motions for FPU lattice systems with asymptotically quadratic potentialsUnnamed ItemHigh-energy waves in superpolynomial FPU-type chainsOn the solitary wave pulse in a chain of beadsNumerical experiments on the modulation theory for the nonlinear atomic chainSpectro-spatial wave features as detectors and classifiers of nonlinearity in periodic chainsTravelling waves for a Frenkel-Kontorova chainAtomic-scale localization of high-energy solitary waves on latticesEnergy thresholds for the existence of breather solutions and travelling waves on latticesDispersive stability of infinite-dimensional Hamiltonian systems on latticesOn the impact of FPU lattice discreteness upon solitary wave interactionsPulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gapOn the existence of solitary traveling waves for generalized Hertzian chainsOn the Korteweg-de Vries limit for the Fermi-Pasta-Ulam systemA uniqueness result for a simple superlinear eigenvalue problemMacroscopic behavior of microscopic oscillations in harmonic lattices via Wigner-Husimi transformsSolitary waves in mass-in-mass latticesSolitary waves on nonlocal Fermi-Pasta-Ulam lattices: exponential localizationOn periodic motions of a two dimensional Toda type chainTravelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interactionMoving discrete breathers?Solitary waves in atomic chains and peridynamical mediaAsymptotic approximations to travelling waves in the diatomic Fermi-pasta-Ulam latticeAsymptotic two-soliton solutions in the Fermi-Pasta-Ulam modelPersistence of supersonic periodic solutions for chains with anharmonic interaction potentials between neighbours and next to nearest neighboursExistence of solitary waves in one dimensional peridynamicsNanoptera in nonlinear woodpile chains with zero precompressionScaling relations for auxin wavesTwo novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam modelTravelling breathers with exponentially small tails in a chain of nonlinear oscillatorsExact Diatomic Fermi--Pasta--Ulam--Tsingou Solitary Waves with Optical Band Ripples at InfinityDispersive fractalisation in linear and nonlinear Fermi–Pasta–Ulam–Tsingou latticesNanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular ChainsConstruction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map latticesExistence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approachSimulation, modeling and dynamical analysis of multibody flowsExistence of generalized solitary wave solutions of the coupled KdV-CKdV system



Cites Work


This page was built for publication: Existence theorem for solitary waves on lattices