Open AccessGeometric solitary waves in a 2D mass-spring lattice
Author(s) -
Gero Friesecke,
Karsten Matthies
Publication year - 2003
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2003.3.105
Subject(s) - anharmonicity , physics , lattice (music) , longitudinal wave , hamiltonian (control theory) , classical mechanics , geometry , condensed matter physics , quantum mechanics , wave propagation , mathematics , acoustics , mathematical optimization
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