Control of localized non-linear strain waves in complex crystalline lattices

The distributed feedback control is developed to support propagation of localized non-linear waves for the double sine-Gordon equation and the dispersive sine-Gordon equation previously obtained for the description of dynamic processes in complex crystalline lattices. The control allows the propagation of both bell-shaped and kink-shaped waves with permanent shape and velocity, with a functional form which does not correspond to the known analytical solutions of the equations. The results might be used for choosing external loading providing desired strain localization or variations in the internal structure of the lattice.