Exact Soliton Solutions to a Generalized Nonlinear Schrödinger 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 Schrodinger 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.