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Nonlinear theory of localized and periodic waves in solid crystal media with complex lattice

The continual nonlinear theory of crystal media with a complex structure of lattice consisting of two sub-lattices were developed in works [1]-[3]. In this work a plane deformation of crystal media with a cubic lattice is considered. Equations of motion of acoustic mode U(x, y, t) are written in the form of the usual equations of the theory of elasticity. Equations of an optical mode u(x, y, t) are a system of two coupled nonlinear Klein-Fock-Gordon equations. Functionally invariant solutions of the system of the equations for a microfield are constructed. Solutions contain two arbitrary functions depending on a certain ansatz α(x, y, t). Dependence of type of wave motion on properties of crystal lattice, external stresses, and potential of interaction between sublattices is investigated.