Study of vortex ring dynamics in the nonlinear schrodinger equation utilizing gpu-accelerated high-order compact numerical integrators

摘要: We numerically study the dynamics and interactions of vortex rings in nonlinear Schrodinger equation (NLSE). Single ring for both bright dark are explored including their traverse velocity, stability, perturbations resulting quadrupole oscillations. Multi-ring investigated, scattering merging two colliding rings, leapfrogging co-traveling as well co-moving steady-state multi-ring ensembles. Simulations choreographed setups also performed, leading to intriguing interaction dynamics. Due inherent lack a close form solution dimensionality where they live, efficient numerical methods integrate NLSE have be developed order perform extensive number required simulations. To facilitate this, compact high-order schemes spatial derivatives which include new semi-compact modulus-squared Dirichlet boundary condition. The combined with fourth-order Runge-Kutta time-stepping scheme keep overall method fully explicit. ensure use schemes, stability analysis is performed find bounds on largest usable time step-size function step-size. The implemented into codes run NVIDIA graphic processing unit (GPU) parallel architectures. running GPU shown many times faster than serial counterparts. future usability mind, therefore written interface MATLAB utilizing custom GPU-enabled C MEX-compiler interface. Reproducibility results achieved by combining code package called NLSEmagic freely distributed dedicated website.