Charge and energy transport by Holstein solitons in anharmonic one-dimensional systems

We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.