As a first step in the search of an analytical study of mechanical denaturation of DNA in terms of the sequence, we study stable, stationary solutions in the discrete, finite and homogeneous Peyrard-Bishop DNA model. We find and classify all the stationary solutions of the model, as well as analytic approximations of them, both in the continuum and in the discrete limits. Our results explain the structure of the solutions reported by Theodorakopoulos {em et al.} [Phys. Rev. Lett. {bf 93}, 258101 (2004)] and provide a way to proceed to the analysis of the generalized version of the model incorporating the genetic information.
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