Analytical solutions to the (3+1)-dimensional generalized nonlinear Schrodinger equation with varying parameters

Analytical solutions to the (3+1)-dimensional nonlinear Schrodinger equation (NLSE) are obtained. It is the first time to our knowledge that analytical solutions to the three-dimensional NLSE with varying coefficients have been derived. The solutions are the generalization of analytical solutions to the one-dimensional NLSE. The properties of the amplitudes and the phases of the solutions are investigated.