NONLINEAR PHYSICS - INTEGRABILITY, CHAOS AND BEYOND

Integrability and chaos are two of the main concepts associated with n onlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often asso ciated with many of the important integrable nonlinear systems while m otions which are sensitively dependent on initial conditions are assoc iated with chaotic systems. Besides dramatically raising our perceptio n of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based info rmation technology, magnetoelectronics, controlling and synchronizatio n of chaos and secure communications, to name a few. These development s have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and pay offs ahead in the next few decades by tracing the early historical eve nts, summarizing the revolutionary era of 1950-1970 when many importan t new ideas including solitons and chaos were realized and reviewing t he cur rent status. Important open problems both at the basic and appl ied levels are discussed. (C) 1997 The Franklin Institute. Published b y Elsevier Science Ltd.