Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation center dot(0)-> 0, where center dot(0) is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without center dot(0)-> 0. The model still supports soliton solutions indexed by two winding numbers (n,m); we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively.