Exact spatiotemporal wave and soliton solutions to the generalized (3 + 1)-dimensional nonlinear Schrödinger equation with linear potential

Exact extended traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with distributed coefficients and linear potential are found. We obtain solutions for four combinations of the temporal dependence of the coefficients: constant and sinusoidal diffraction coefficients and constant and sinusoidal external electric fields. A number of stable periodic soliton solutions are obtained whose signal does not decrease with time in the absence of an externally induced loss.