Stable Structures of Nonlinear Parabolic Equations with Transformation of Spatial Variables

Problem review of existence and stability nonlinear parabolic functionally differential equations structures with transformation of spatial variables. Such equations model optical systems that contain a thin layer of a nonlinear Kerr-type medium. Review of Initial boundary value problems for circumference, a circle, and a ring with an involution operator, corresponding to transformation of variables (rotation). The asymptotics of solutions are constructed using the method of central manifolds. Analysis of Metastable structures and slowly changing solutions. Approximate solutions are found using Galerkin approximations. Presentation of the results for numerical experiments.