Kink-antikink collisions in sine-Gordon andφ4models: Problems in the variational approach

In this paper, a collective-coordinate description of a breatherlike solution of the perturbed sine-Gordon equation is considered. It is shown both numerically and analytically that the equations describing the evolution of the breather parameters are ill defined. This feature is shown to arise because the equations are obtained through a projection on a null vector. It is shown to be present also in collective-coordinate descriptions of the kink-antikink collision in the ${\mathrm{\phi }}^4$ model. Alternative Ansa$uml—tze hat do not cause singularities are presented.