Geometric solitary waves in a 2D mass-spring lattice

Gero Friesecke; Karsten Matthies

doi:10.3934/dcdsb.2003.3.105

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2003, Volume 3, Issue 1: 105-114. Doi: 10.3934/dcdsb.2003.3.105

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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

Received: December 31, 2001

Revised: May 31, 2002

Published: January 2003

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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.

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Mathematics Subject Classification: 37K60, 74J35, 74J30.

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