Application of Python 3.9 framework to investigate the dynamics of vortex-solitons

Abstract

In our study the stability of solitons of the nonlinear Schrodinger equation is investigated via the computation the dynamics of vortex rings. To do that we use the modern PY-PDE package in the framework of Python 3.9. The main purpose of this package is to simulate the partial differential equations (PDE) in simple geometry. Temporal evolution of the PDE is determined using the line method by explicitly sampling space, using fixed grids with simultaneous temporal visualization of dynamics. Such a system supports the use of object-oriented programming and the numba-compiled method to speed up computations. With the use of PY-PDE package we numerically investigate the dynamic phenomenon in a Bose-Einstein condensate (BEC) placed in an external potential. The same model can also be applied to study the spatial electromagnetic solitons in fibers. Both the one-dimensional and two-dimensional cases are considered.

Keywords

• Fiber
• solitons
• nonlinear Schrödinger equation
• dynamics