On radial sine-Gordon breathers

The problem of the existence of radial sine-Gordon breathers (i.e. radial solutions which are periodic in time and decay at infinity with respect to the spatial variable) in the (d + 1)-dimensional case (where d > 1) is considered. We have constructed numerically such entities which have infinite energy; simultaneously, Re give a numerical confirmation of the non-existence of such objects with finite energy. We offer an interpretation of the observed robustness of such entities as seen in numerical simulations. It is based on our numerical analysis of the problem in a bounded domain, 0 < r < R, and with non-integer values of d. AMS classification scheme numbers: 35L70, 35Q53, 81T80, 34C35.