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The article coments on the analytical and numerical methods of control transformation problem in the space arguments, and differential equations. The paper suggests the control problem statement of a two-dimensional transformation for the spatial arguments and the analysis of its properties like uniform quasidifferentiability of the objective function, its gradient HÖlder condition, the gradient projection method convergence, and the control problem solvability on a compact set.

Presents the rotating structures in a parabolic functional-differential equation. Mathematical model of a nonlinear optical system; Existence and uniqueness of time-periodic solutions; Properties of the semigroup generated by the problem; Introduction of the Hilbert space of measurable functions.

Considers the interaction of traveling waves in a parabolic functional-differential equation. Features of the mathematical model of the nonlinear optical system; Relationship between the problem on the appearance of rotating waves in an optical system and the bifurcation of t-periodic solutions in a neighborhood of a stationary spatially homogenous mode of the equation.