Spatiotemporal similariton interactions in a linear potential

We derive a series of analytical solutions that describe spatiotemporal solitons and similaritons for the generalized (3 + 1)-dimensional nonlinear Schrodinger equation with a linear potential. The explicit functions that describe the evolution of the width, peak and phase are obtained exactly. The gain parameter has no effect on the motion of the soliton's or similariton's phase or their widths, and it affects just the evolution of their peaks. In the constant parameter system, the effect of the chirp is not only to reduce the intensity but also to change the dynamic evolution of the velocities. In the periodic system, the effect of adding chirp influences the oscillating degree of the similariton's peak.