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February  2003, 3(1): 105-114. doi: 10.3934/dcdsb.2003.3.105

Geometric solitary waves in a 2D mass-spring lattice

Gero Friesecke 1, and  Karsten Matthies 1,

1. 

Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom, United Kingdom

Received  January 2002 Revised  June 2002 Published  November 2002

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.
Keywords: geometric nonlinearity., many-particle systems, solitary waves, Lattice dynamics.
Mathematics Subject Classification: 37K60, 74J35, 74J3.
Citation: Gero Friesecke, Karsten Matthies. Geometric solitary waves in a 2D mass-spring lattice. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 105-114. doi: 10.3934/dcdsb.2003.3.105
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