Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with space-dependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with w
ells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.
This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalised angular momentum or grand spin. It can be solved explicitly for a Skyrme co
nfiguration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterised by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta function regularization.
