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.
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - Feb 2003|
Friesecke, G., & Matthies, K. (2003). Geometric solitary waves in a 2D mass-spring lattice. Discrete and Continuous Dynamical Systems - Series B, 3(1), 105-144. https://doi.org/10.3934/dcdsb.2003.3.105