ASYMPTOTIC-BEHAVIOR OF ONE-DIMENSIONAL NONLINEAR DISCRETE KINK-BEARING SYSTEMS IN THE CONTINUUM-LIMIT - PROBLEMS OF NONUNIFORM CONVERGENCE

We study the validity of perturbational treatments of one-dimensional weakly discrete kink-bearing systems with the corresponding continuum model as the unperturbed state. We calculate the Peierls-Nabarro barrier height DELTA(PN), the Peierls-Nabarro frequency omega(PN), and the deviation of the kink creation energy from the continuum case. In the case of the sine-Gordon system and the PHI4 system, we find that the dressing (change of the continuum kink shape due to discreteness) contributes to the values of DELTA(PN) and omega(PN) through all orders of perturbation, thereby making the whole perturbation scheme irrelevant. In contrast, the double-quadratic model (where the whole necessary nonlinearity is ''hidden'' in one nonanalytic point) can be treated by the perturbation scheme without restrictions. The results found in this paper put general limitations on analytical approaches to nonlinear phenomena in discrete systems and demonstrate a deep inherent difference between corresponding discrete and continuum models.