Asymptotic Approximation of Discrete Breather Modes in Two-Dimensional Lattices
نویسنده
چکیده
We outline the small amplitude asymptotic approximation for breathers for one-dimensional chains, and two-dimensional lattices with square, triangular/hexagonal, and honeycomb geometries. Two-dimensional lattices are complicated due to the resulting NLS-type equation being either elliptic or hyperbolic in nature. This gives rise to an additional constraint in addition to the usual condition on the relative strengths of quadratic and cubic nonlinearities. The honeycomb lattice requires a more advanced approach since it has a diatomic nature. Results from the three geometries are compared.
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