Approximations to solitary waves on lattices. II. quasi-continuum methods for fast and slow waves

DOI10.1088/0305-4470/26/5/036zbMath0774.35069OpenAlexW2092324331MaRDI QIDQ4694866

Jonathan A. D. Wattis

Publication date: 17 August 1993

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/26/5/036

zbMATH Keywords

accurate analytic expressions for the size and shape of solitary waves on lattices with nonharmonic interactions

Mathematics Subject Classification ID

Soliton equations (35Q51) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (18)

Existence theorem for solitary waves on lattices ⋮ Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain ⋮ Solitary waves in FPU-type lattices ⋮ Quasicontinuum models of dynamic phase transitions ⋮ Periodic traveling waves in the system of linearly coupled nonlinear oscillators on 2D-lattice ⋮ An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices ⋮ Solitary wave propagation in a two-dimensional lattice ⋮ Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices ⋮ Mobility of lattice defects: Discrete and continuum approaches. ⋮ Strictly supersonic solitary waves in lattices with second-neighbor interactions ⋮ Continuous models for 1D discrete media valid for higher-frequency domain ⋮ Approximations of solitary waves on lattices using weak and variational formulations ⋮ Improved continuous models for discrete media ⋮ Behaviour of the extended Volterra lattice ⋮ Asymptotic approximations to travelling waves in the diatomic Fermi-pasta-Ulam lattice ⋮ Dynamics in a confined mass-spring chain with \(1/r\) repulsive potential: strongly nonlinear regime ⋮ Dispersive shock waves in lattices: a dimension reduction approach ⋮ Solitons on lattices

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