A.S. Kryukovsky, D.S. Lukin, Yu.V. Saren

The influence of thermal nonlinearity on structure of an electromagnetic field in focal regions such as catastrophes is investigated. The numerical modeling of deformation of a wave field structure at change of a nonlinearity parameter is executed by a method of the parabolic equation in focal regions appropriate to a cuspoid singularity such as "butterfly". Bifurcations of singularities are investigated. The concept of the associated ray structure of a field is entered and the qualitative conformity of development of amplitude and ray structure of a field with increase of a parameter of nonlinearity is shown. The development of singularity (catastrophe), crushing of amplitude structure and formation of the new focal centers are investigated.