The relevance of nonlinear stacking interactions in simple models of double-stranded DNA

Single molecule DNA experiments provide interesting data that allow a better understanding of the mechanical interactions between the strands and the nucleotides of this molecule. In some sense, these experiments complement the classical ones about DNA thermal denaturation. It is well known that the original Peyrard-Bishop (PB) model by means of a harmonic stacking potential and a nonlinear substrate potential has been able to predict the existence of a critical temperature of full denaturation of the molecule. In the present paper, driven by the findings of single molecule experiments, we substitute the original harmonic intra-strand stacking potential with a Duffing type potential. By elementary and analytical arguments, we show that with this choice it is possible to obtain a sharp transition in the classical domain wall solution of the PB model and the compactification of the classical solitary wave solutions of other models for the dynamics of DNA. We discuss why these solutions may improve our knowledge of the DNA dynamics in several directions.