Quasisoliton states in a two-dimensional discrete model

We present a numerical study of a two-dimensional discrete model for the interaction between an excitation and the phonons in the adiabatic limit. The static stable configuration has been found by a steepest-descent algorithm while the equations of motion have been integrated by the Runge-Kutta method. The ground-state configuration shows a self-trapping transition for a critical value of the coupling constant, while the time evolution from an initial localized excitation has solitonlike features in a certain range of the parameters. The dynamical simulation results have strong similarities to the ones obtained in the framework of the one-dimensional Davydov model. An extensive threshold study for the soliton generation is also reported. The possible physical implications of our work are discussed especially in connection to the charge transport in the cuprate superconductors.