Nanosecond dynamics of solitons in confined Bose-Einstein condensates

Nanoscale anisotropic dynamical systems are tedious to solve in a classical domain without any approximation techniques. In such cases, the interactive space and force are significant in defining their motions. We solve and simulate the phase transition motion of water in the interface of 3 μm × 3 μm confined water domain. We demonstrate the presence of solitons in Bose-Einstein condensate at a nanosecond time scale by solving a nonlinear partial differential equation. We find an exact solution of the 2D Gross-Pitaevskii equation with XY-model using the Heisenberg picture which creates solitons and condensate nucleation.