Spatiotemporal breather in diffraction decreasing media

• Spatiotemporal breathers of 3DNLSE with different transverse diffractions is derived.
• Controllable breathers by adjusting the relation between parameters TmTm and T0T0.
• Controllable behaviors includes initial and fast excitation, sustainment and restraint.

The similarity transformation between the (3+13+1)-dimensional nonlinear Schrödinger equation with different distributed transverse diffraction and the standard nonlinear Schrödinger equation is found, and a spatiotemporal breather solution is given based on this transformation. The control for the evolutional behaviors of a spatiotemporal breather is discussed. Our results manifest that the relation between the maximum accumulated time TmTm and the accumulated time, T0T0, with the maximum amplitude, is the basis to realize the control and manipulation of propagation behaviors of breathers, such as fast and slow excitations, sustainment and restraint. These results are potentially useful for future experiments in the optical communications and Bose–Einstein condensations.