HIGH-ORDER BREATHER SOLUTIONS TO A DISCRETE NONLINEAR KLEIN-GORDON MODEL

A general discrete nonlinear Klein-Gordon model is studied with regards to the movability of breathers. Approximations to moving breather solutions are found by a semi-discrete multiple-scale perturbation expansion to 3rd order. The higher order effects of discreteness have a remarkable connection to nonlinear fiber optics. Effects such as higher order dispersion, self-steepening of the pulse edge, and self-frequency shift are found, modifying both the shape, velocity and frequency of the solution. Here only their combined influence is studied. Discreteness is found to trap breathers with initial amplitudes higher than a critical value, which depends on the internal state of the breather. This shows that no strict definition of the Peierls-Nabarro potential can be given for breathers. Furthermore, we find that the envelope velocity of the breather cannot exceed the maximum group velocity which converges to zero as the degree of discreteness is increased. Thus no moving breathers exist in a highly discrete system.