Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model

We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.