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 l0 --> 0, where l0 is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without l0 --> 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.