Nonlinear physics: integrability, chaos and beyond

Lakshmanan, M. (1997) Nonlinear physics: integrability, chaos and beyond Journal of the Franklin Institute, 334 (5-6). pp. 909-969. ISSN 0016-0032

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Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-1970 when many important new ideas including solitons and chaos were realized and reviewing the current status. Important open problems both at the basic and applied levels are discussed.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:19626
Deposited On:22 Nov 2010 12:16
Last Modified:17 May 2016 04:08

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