Geometric solitary waves in a 2D mass-spring lattice

Gero Friesecke; Karsten Matthies

doi:10.3934/dcdsb.2003.3.105

Geometric solitary waves in a 2D mass-spring lattice

Gero Friesecke, Karsten Matthies

Department of Mathematical Sciences

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Abstract

The existence of longitudinal solitary waves is shown for the Hamiltonian dynamics of a 2D elastic lattice of particles interacting via harmonic springs between nearest and next nearest neighbours. A contrasting nonexistence result for transversal solitary waves is given. The presence of the longitudinal waves is related to the two-dimensional geometry of the lattice which creates a universal overall anharmonicity.

Original language	English
Pages (from-to)	105-144
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	3
Issue number	1
DOIs	https://doi.org/10.3934/dcdsb.2003.3.105
Publication status	Published - Feb 2003

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10.3934/dcdsb.2003.3.105

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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version Friesecke, G & Matthies, K 2003, 'Geometric solitary waves in a 2D mass-spring lattice' Discrete and Continuous Dynamical Systems - Series B, vol 3, no. 1, pp. 105. is available online at: http://dx.doi.org/10.3934/dcdsb.2003.3.105
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Geometric solitary waves in a 2D mass-spring lattice

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