Evolution of the exact spatiotemporal periodic wave and soliton solutions of the (3Â +Â 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

► The (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients is solved analytically by an improved homogeneous balance principle and F-expansion technique, where the diffraction coefficient and dispersion coefficient are considered to be two different functions. Then, the propagation characteristics of the exact solutions are analyzed in detail. ► The evolutions of propagation of the exact solutions are regular when the diffraction and dispersion coefficients are the identical distributed coefficients. ► The evolutions of propagation of the exact solutions are irregular with other coefficients.