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January 1, 2003Discrete and Continuous Dynamical Systems - BOpen Access

Geometric solitary waves in a 2D mass-spring lattice

Gero Friesecke Karsten Matthies

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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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Friesecke et al. (2003) studied this question.

synapsesocial.com/papers/69ffdeec7ac91c5d2a2d63d6 https://doi.org/10.3934/dcdsb.2003.3.105

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