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Geometric solitary waves in a 2D mass-spring lattice

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


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