Vortex solitons in the (2 + 1)-dimensional nonlinear Schrödinger equation with variable diffraction and nonlinearity coefficients

Using Hirota's bilinear method, we determine approximate analytical localized solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with variable diffraction and nonlinearity coefficients. Our results indicate that a new family of vortices can be formed in the Kerr nonlinear media in the cylindrical geometry. Variable diffraction and nonlinearity coefficients allow utilization of the soliton management method. We present solitary solutions for two types of distributed coefficients: trigonometric and exponential. It is demonstrated that the soliton profiles found are structurally stable, but slowly expanding with propagation.