In this paper, we present a non-linear model for the study of DNA denaturation transition. To this end, we assume that the double-strands DNA interact via a realistic generalized Morse potential that reproduces well the features of the real interaction. Using the Transfer Matrix Method, based on the resolution of a Schrödinger equation, we first determine exactly their solution, which are found to be bound states. Second, from an exact expression of the ground state, we compute the denaturation temperature and the free energy density, in terms of the parameters of the potential.Then, we calculate the contact probability, which is the probability to find the double-strands at a (finite) distance apart, from which we determine the behaviour of the mean-distance between DNA-strands.The main conclusion is that, the present analytical study reveals that the generalized Morse potential is a good candidate for the study of DNA denaturation
Sharp DNA denaturation in a helicoidal mesoscopic model
