Numerical investigation of highly excited magnetic monopoles in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Yang-Mills-Higgs theory

Preliminary results concerning the time evolution of strongly exited $SU(2)$ Bogomolny-Prasad-Sommerfield (BPS) magnetic monopoles have been published in G. Fodor and I. R\'acz, Phys. Rev. Lett. 92, 151801 (2004). The behavior of these dynamical magnetic monopoles was investigated by means of numerical simulations in the four-dimensional Minkowski spacetime. The developed code---although applied to spherically symmetric configurations---incorporates both the techniques of conformal compactification and that of the hyperboloidal initial value problem. Our primary aim here is to provide a detailed account on the methods and results of the investigations reported in G. Fodor and I. R\'acz, Phys. Rev. Lett. 92, 151801 (2004). In addition, some important new results, which go much beyond the scope of these early studies, are also presented. In particular, to be able to distinguish linear and nonlinear effects, evolutions of monopoles deformed by various excitations, including both very small and extra large energy excitation, are investigated. In addition, a detailed account is provided on the spacetime dependence of the basic variables, as well as that of the other physically significant dynamical qualities such as the energy and energy current densities, the radial and angular pressures, and the magnetic charge density. A careful comprehensive study of the associated energy transfers and energy balances is also included.