The ϕ4 Oscillons in a Ball: Numerical Approach and Parallel Implementation

Weakly radiating spherically-symmetric oscillons in the model can be approximated by standing waves in a ball of a finite radius. Temporally periodic standing waves are then determined as solutions of the boundary-value problem posed on a cylindrical surface, and their stability is classified by evaluating the associated Floquet multipliers. In this contribution we provide details of this numerical approach and present results on the spatio-temporal structure and bifurcation of the standing waves. We also discuss the parallel implementation of the Floquet multipliers calculation algorithm using resources of the JINR Multifunctional Computing Complex.