New exact and approximate stationary solutions of (1+2)D nonlinear Schrödinger equation in dual-power media

In the paper propagation of axially-symmetric (1+2)D beam in nonlinear medium with dual-power nonlinearity is analyzed. The ordinary differential equation for transverse stationary profile of the propagating field is derived and solved using a perturbation technique. The simple analytical formulas for the three lowest order solutions are obtained. They describe fields of algebraic profiles. The zero order solution satisfies exactly the nonlinear Schrödinger equation in (1+2)D case. Higher order solutions are determined by propagation constant and describe fields of different initial amplitude. The accuracy of approximation and stability of the obtained solutions are discussed.