Soliton structure dynamics in inhomogeneous media

We show that soliton interaction with finite-width inhomogeneities can activate a great number of soliton internal modes. We obtain the exact stationary soliton solution in the presence of inhomogeneities and solve exactly the stability problem. We present a Karhunen–Loève analysis of the soliton structure dynamics as a time-dependent force pumps energy into the translational mode of the kink. We show the importance of the internal modes of the soliton as they can generate shape chaos for the soliton as well as cases in which the first shape mode leads the dynamics.