Frequency–momentum representation of moving breathers in a two dimensional hexagonal lattice

We study nonlinear excitations propagating in a hexagonal layer which is model for the cation of silicates. consider their properties frequency-momentum or $\omega-k$ representation, extending theory on pterobreathers moving frame first time to two dimensions. It can also be easily extended three Exact traveling waves representation are within {\em resonant} planes, each plane corresponding single frequency. These frequencies integer multiples frequency called fundamental A breather resonant and has frame. The intersection planes with phonon surfaces produce co-traveling wings small set frequencies. obtained by perturbing system consist soliton together quasi-exact. used as seeds obtain exact waves, formed soliton. do exist but they usually very small.