New classes of stable exact solutions for a nonlinear rotational DNA model

Abstract

We consider a system of two coupled nonlinear partial differential equations for describing the rotational motions of bases in both polynucleotide chains of the DNA molecule. The model was proposed by L.V. Yakushevich and it is well known that the model supports, for some operating regimes, traveling wave solutions as kink–(antikink) soliton solutions. We have tried to make some progress by performing an analysis of the classical symmetries of this model. Our study shows that the model does not have enough symmetries as to reduce the equations to ordinary differential equations. Nevertheless, the known symmetries have been useful for finding several classes of exact solutions, by imposing adequate Ansätze. Some of them are kink–(antikink) like solutions, but other ones are not traveling wave solutions. For some of the new solutions, we have carried out a qualitative study and analyzed some stability properties. We think that they could be significant for the description of the DNA molecule as well as for some other applications.