Exact traveling wave solutions in the coupled plane-base rotator model of DNA

•Traveling soliton like solutions in nonlinear physics.•Transmitting information with the aid of soliton like structures in DNA.•Generalized coherent state approach for quasi spin Hamiltonians.

The internal dynamics of the DNA base pairs is studied starting from the generalized coupled plane base-rotator model of DNA, obtained by Yomosa and later improved by Takeno and Homma. We conceive the double-stranded DNA as an anisotropically coupled spin chain simple model. The generalized Hamiltonian expressed in terms of quasi-spin operators is averaged over the generalized coherent states in the Perelomov sense, in order to obtain the classical non-linear evolution equations of this molecular system where the inhomogeneity has not been considered. This approach provides the equations of motion, which could be reduced to a nonlinear Schrödinger equation with a saturable nonlinearity. This non-linear equation, under certain restrictions in the parametric space, supports traveling periodic triangular, bell, bubble and kink like solutions.