Solitons in Synthetic and Biological Polymers

Abstract

Nonlinear science has, in recent years, begun to receive truly interdisciplinary attention and to involve a supporting interplay of analysis, computation and experiment. Most of the problems being addressed have a long history but are now benefiting from this new interdisciplinary view. The synergistic impact of computers plays an increasingly important role and there are some new concepts —solitons, toplogy, “universal” routes to chaos and its characterization, pattern selection and evolution, etc. Significant advances have occurred in our appreciation for the consequences of strongly nonlinear phenomena and our ability to experimentally detect them. In particular the “soliton paradigm”¹ has acquired, in the space of a decade, an astonishing list of applications across the natural sciences. Our focus here is only a small subset of these applications but already vast: namely applications in solid state materials and of those primarily low-dimensional examples (weakly coupled chains or layers). Furthermore, we will not discuss any problems arising in nonlinear diffusion equations, although these are fundamental in their own right for descriptions of reaction-diffusion systems, interface dynamics, nerve-pulse propagation, etc.²