Abstract
Weakly radiating spherically-symmetric oscillons in the \({{\phi }^{4}}\) theory can be approximated by standing waves in a ball of a finite radius. We determine the temporally periodic standing waves as solutions of a boundary-value problem on the two-dimensional domain \([0,T] \times [0,R]\) where \(T\) is the period of oscillations and \(R\) radius of the ball. We implement the Newtonian iteration with the 4th order finite difference approximation. The stability of standing waves is classified by evaluating the associated Floquet multipliers. The multipliers are calculated, in parallel, using resources of the JINR multifunctional computing complex. We present a description of our numerical approach and obtained results. We discuss the dependence of structure and properties of standing waves on \(R\) and \(T\) .
