Global coordinates for the breather-kink (antikink) sine-Gordon phase space: An explicit separatrix as a possible source of chaos

Abstract

In this paper we present global coordinates for the kink-antikink breather sine-Gordon phase space with a separatrix and singular points. Using these coordinates we derive reduced equations governing perturbed dynamics, and we use them in a Melnikov calculation to establish the presence of chaos in the reduced sine-Gordon system.