J. Engelbrecht - Böcker

The general idea advocated in this work is to start from complicated mathematical models describing wave motion as it results from the rules of continuum mechanics, and then to find a simpler viewpoint that still keeps everything essential preserved. Special attention is paid to the description of the sources of nonlinearities. The complexities in modelling are demonstrated by several examples including solitons, propagating instabilities and waves in waveguides. The selected case studies show some unconventional approaches in order to explain the richness of nonlinear wave motion. The final chapters are of more general character, including the essays on nonlinearity, beauty, and complexity. In this way, the thread of the analysis is the following: simple basic arguments result in a complicated theory that, in turn, needs certain simplifications in order to grasp the physical phenomena involved. What makes this book special compared to other books in the field is that all the examples are cast into a general philosophical network of complexity and simplicity.

Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Besides fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up-to-date account of the current state of research in the theory and practice of nonlinear waves in solids.

Recent progress in the study of nonlinear wave propagation has been influenced by developments in mechanics, acoustics, hydro­ dynamics, plasma physics and many other fields of physics. This vast field of research has also given rise to fascinating mathe­ matical ideas: the inverse scattering method and the technique of exterior differential forms being just some to be mentioned. Obviously the theory of nonlinear waves may be interpreted as an interdisciplinary study with the mechanics of continuous media as a theoretical basis. This was the starting point of the proposal to the General Assembly of the IUTAM to hold an IUTAM Symposium on this topic, made by the USSR National Committee of Theoretical and Applied Mechanics and the Academy of Sciences of the Estonian SSR. Actually the IUTAM Symposium on Nonlinear Deformation Waves was the third meeting of such kind to be held in Tallinn. In 1973, the Academy of Sciences of the Estonian SSR and Gorky State University or~anized a national Symposium on Nonlinear and Thermal Effects in Transient Wave Propagation. In 1978, the Academy of Sciences of the Estonian SSR organized another national Symposium on Nonlinear Deformation Waves with partici­ pants from several other countries. The participants of this Symposium in their final resolution expressed a wish that a similar meeting of definitely international type should take place again in Tallinn in 1982.