The study of nonlinear systems is currently one of the most exciting and fastest growing branches of the mathematical sciences. It has led both to major developments in the theoretical understanding of such systems, and to an increasing awareness of the importance of these results to a wide variety of applied disciplines, including the physical and biological sciences, most branches of engineering and information technology and potentially even economics and the social sciences. Nonlinear mathematics offers these subjects new models and paradigms, provides fresh insights into previously poorly understood phenomena and makes available novel techniques for their investigation and explanation. One might say that nonlinear mathematics is in fact a whole new way of thinking.
The importance of nonlinearity to applications cannot be overemphasised; nonlinear systems are capable of behaviour quite unknown in linear systems. Moreover, most systems, both natural and man-made, exhibit nonlinear features to some degree. Nature has never paid any respect to the dogma of linearity, and thus as the sciences seek an ever better understanding of the real world, they are forced to take more and more account of nonlinearity. Similarly, whilst the majority of engineering systems might be designed to be as linear as possible, they will inevitably enter non-linear regimes if, for instance, driven at sufficiently high amplitudes, or even through interactions with their environment. Furthermore nonlinearity offers new opportunities to the system designer for achieving novel effects or levels of performance. Today's engineer must pay at least as much attention to nonlinearity as his scientific colleague.
Conversely, in many cases, the consideration of specific applications can inspire new developments in mathematics. Thus many of Poincaré's most fundamental contributions were motivated by celestial mechanics, whilst Cartwright and Littlewood (and hence indirectly Smale) were motivated by problems in radar. More recently, the effect on mathematics of the work of Lorenz can hardly be overstated. Mathematics therefore has as much to gain from interactions with other disciplines as the other way round.
The UK has a strong and active nonlinear community, on both the applied and theoretical sides. However, for some time there has been a widespread feeling that its is becoming increasingly difficult for different groups in this area to keep abreast of the wide variety of nonlinear activities throughout the country. This newsletter is an attempt to alleviate this communication gap and to provide a forum for informal contact between all those who have an interest in nonlinear science. Broadly speaking we hope that each issue will carry several articles about various groups and activities, as well as shorter pieces of news, reviews, questions, and anything else that you think others might find interesting.
Clearly this endeavour depends for its success on the active participation of the nonlinear community. So please let us know what you find useful, and what you would like to see, and above all please submit articles and other news of your activities to us. Although primarily we intend this newsletter to be a service to the UK community, this should not be seen as exclusive, and participation from overseas will also be very welcome.
The editors Friday, June 16, 1995.
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Last Updated: 19 June 1995.