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

A general discrete nonlinear Klein-Gordon model is studied with regard s to the movability of breathers. Approximations to moving breather so lutions are found by a semi-discrete multiple-scale perturbation expan sion to 3rd order. The higher order effects of discreteness have a rem arkable connection to nonlinear fiber optics. Effects such as higher o rder 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. Discreten ess is found to trap breathers with initial amplitudes higher than a c ritical value, which depends on the internal state of the breather. Th is shows that no strict definition of the Peierls-Nabarro potential ca n be given for breathers. Furthermore, we find that the envelope veloc ity of the breather cannot exceed the maximum group velocity which con verges to zero as the degree of discreteness is increased. Thus no mov ing breathers exist in a highly discrete system.