Complex representation of general solution of the nonlinear equations for deformation of crystal media with a complex lattice is given for a case of plane deformation. Expressions for acoustic and optical modes, as well as for tensors of macro- and microdeformations are obtained having applied arbitrary functions of a complex variable. They are similar to the Kolosov-Muskhelishvili formulas in the presence of bulk sources. In the nonlinear model, a role of bulk sources is played by microshifts u_s along a vector of the inverse lattice. The value u_s is found from the solution of a nonlinear equation of sine-Gordon type. The obtained complex representations of the general solution of the nonlinear equations allows us to apply the theory of functions of a complex variable to the solution of specific problems of the plane deformation theory.
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