Abstract
We consider a sine-Gordon model in 1 + 1 dimensions modified by the addition of a further kinetic term similar to the Skyrme term in higher dimensions and an extra potential term. The model has interesting properties. In particular, in addition to the familiar sine-Gordon soliton it possesses a double-kink solution which has an internal oscillatory mode. The sine-Gordon kink has a definite velocity and this velocity is a critical velocity for the double-kink structures. For some range of the parameters the model has two different solutions, with the same boundary conditions, which propagate at the velocity of the sine-Gordon kink. When the exact solutions are perturbed or acted upon by an external force they radiate short wavelength oscillations and keep a velocity which remains below the critical value. The same radiation can also stabilize the speed of π-kink solutions for which the boundary conditions correspond to two different levels of the potential energy.
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