Nonautonomous Breather and Rogue Wave in Spinor Bose-Einstein Condensates with Space-Time Modulated Potentials

To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose-Einstein condensates with spatiotemporal modulation, we focus on a system of three coupled Gross-Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions. With different external potentials and gain-loss distributions, various solutions for controlled nonautonomous matter-wave breathers and rogue waves are derived by the Darboux transformation method, such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories. Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied. Nonautonomous two-breathers on the arched and constant backgrounds are also derived.

Automated summary

In this study, we investigate the controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose-Einstein condensates with spatiotemporal modulation. By focusing on a system of three coupled Gross-Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions, we derive various solutions for controlled nonautonomous matter-wave breathers and rogue waves using the Darboux transformation method. We find breathers and rogue waves with periodic and parabolic trajectories on arched and constant backgrounds. The effects of gain-loss distribution and linear potential on these solutions are studied, and nonautonomous two-breathers on arched and constant backgrounds are also obtained.