Hamiltonian dynamics of the double sine-Gordon kink.

Abstract

We present a complete Hamiltonian treatment of a kink with an internal degree of freedom, namely the double sine-Gordon (DSG) kink. In this formalism we assign two canonical coordinates and their associated momenta to describe the motion of the center of mass of the DSG kink and the relative motion of its two subkinks. We show that the canonical coordinate representing the separation of the two subkinks describes a nonlinear oscillatory degree of freedom. Consequently, the DSG kink behaves like a ``molecule'' (4\ensuremath{\pi} kink) comprised of two ``atoms'' (each of a single 2\ensuremath{\pi} kink) held together by a nonlinear potential. As an application of our formalism, we obtain the solutions for the nonlinear internal motion of the DSG in the absence of the radiation field.