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.DGYCYT project MTM2006-05031Junta de Andalucía FQM 201. P06-FQM-0144
