Three-wave parametric simultons in nonlinear lattices

A new type of nonlinear excitations, i.e. three simultaneous lattice solitons (simultons), in a nonlinear diatomic lattice is predicted. We show that three-wave resonance condition can be fulfilled in the diatomic lattice. Using a quasi-discrete multi-scale method we derive nonlinear amplitude equations for the three-wave resonance with the dispersion of the system taken into account. We provide several types of exact lattice simultons solutions and show that the lattice simultons can be non propagating and their oscillating frequencies may be within the gap of phonon spectrum bands.