Exact Soliton Solutions to a Generalized Nonlinear Schrodinger Equation

The （1＋1）-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general （3＋1）-dimensional nonlinear Schr6dinger equation （NLSE） with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The （3＋1）D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.