Crystals with the complex lattice consisting from two sublattices are considered. Big shifts of the sublattices are investigated. The additional element of translation symmetry is put in a basis of creation of the nonlinear theory. It is characteristic for complex lattices, but earlier not entered in solid states physics. Flat and two-dimensional problems are solved for superthin crystal layers in which effects of nanoscale interactions take place. The discrete forces are considered. They are cause of boundary reorganization of molecular structure together with the continuous forces. Also numerical solutions on distribution of shock surface waves such as kinks and solitons, and also the surface perturbations are considered.