Numerical study of the ф4 standing waves in a ball of finite radius

Abstract

Study of spherically symmetric time-periodic standing waves of the \( \varphi^4 \) model in a ball of finite radius was carried out based on the numerical solution of a boundary value problem on a cylindrical surface for a wide range of values of the oscillation period. The standing waves in a ball of finite radius can be considered as an approximation of weakly radiating spherically symmetric oscillons in the \( \varphi^4 \) model. Stability analysis the waves obtained is based on the calculation of the corresponding Floquet multipliers. In the paper, mathematical formulation of the problem is given, the numerical approach is described, including the method of parallel implementation of the calculation of Floquet multipliers on the computing resources of the HybriLIT platform of the Multifunctional Information and Computing Complex of the Joint Institute for Nuclear Research (Dubna). The results of the study of the space-time structure and bifurcation of coexisting standing waves of various types are presented.

Keywords

• oscillons
• numerical study
• parallel computing