Spatiotemporal Rogue Waves for the Variable-Coefficient (3+1)-Dimensional Nonlinear Schrodinger Equation

With the help of the similarity transformation connected the variable-coefficient (3+1)-dimensional nonlinear Schrodinger equation with the standard nonlinear Schrodinger equation, we firstly obtain first-order and second-order rogue wave solutions. Then, we investigate the controllable behaviors of these rogue waves in the hyperbolic dispersion decreasing profile. Our results indicate that the integral relation between the accumulated time T and the real time t is the basis to realize the control and manipulation of propagation behaviors of rogue waves, such as sustainment and restraint. We can modulate the value T-0 to achieve the sustained and restrained spatiotemporal rogue waves. Moreover, the controllability for position of sustainment and restraint for spatiotemporal rogue waves can also be realized by setting different values of X-0.