Towards soliton solutions of a perturbed sine-Gordon equation

We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. Such solutions are allowed exactly by the energy balance of these terms, and can be observed experimentally e.g. in the Josephson effect in the theory of superconductors, which is one of the physical phenomena described by the equation.