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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Geometric solitary waves in a 2D mass-spring lattice

Pages: 105 - 144, Volume 3, Issue 1, February 2003      doi:10.3934/dcdsb.2003.3.105

 
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Gero Friesecke - Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email)
Karsten Matthies - Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email)

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.

Keywords:  Lattice dynamics, many-particle systems, solitary waves, geometric nonlinearity.
Mathematics Subject Classification:  37K60, 74J35, 74J30.

Received: January 2002;      Revised: June 2002;      Available Online: November 2002.