Nonautonomous spatiotemporal solitons in inhomogeneous nonlinear media with linear and nonlinear gain/loss and different distributed diffraction/dispersion

We analytically derive nonautonomous spatiotemporal soliton solutions of the (3 + 1)-dimensional inhomogeneous nonlinear Schrödinger equation with linear and nonlinear gain/loss and different distributed diffraction/dispersion from two kinds of variable transformation connected with a solvable differential equation. Diffraction/dispersion and nonlinearity play important roles in the evolutional characteristics such as amplitude, width, time shift, linear and nonlinear chirp phase, phase offset and phase shift. Diffraction and dispersion management of spatiotemporal solitons with and without nonlinear chirp factor is discussed in a decreasing diffraction/dispersion fiber with exponential, hyperbolic, logarithmic, Gaussian and linear profiles and a periodic modulated system. In a decreasing diffraction/dispersion fiber with exponential profile, the nonlinear chirp factor affects the trace of propagation and the amplitude of the soliton, while the nonlinear chirp factor only influences the amplitude of the soliton in other media. Moreover, we discuss the impact of nonlinear chirp phase on the total phase of spatiotemporal bright and dark solitons. (paper)