Solitary nonlinear Bloch waves

The nonlinear Bloch's theorem for the fundamental and high-order Schrodinger solitons in periodic dispersive and nonlinear structures has been proven. It is shown that bright and dark solitary nonlinear Bloch's waves exist only under certain conditions and that the parameter functions describing dispersion and nonlinearity periodic inhomogeneities cannot be chosen independently. The formation, interaction and stability of the fundamental and high-order solitary nonlinear Bloch waves have been investigated.