A Nonlinear Progress to Modern Soliton Theory
This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction.
Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.
Colin Rogers is an Emeritus Professor at the University of New South Wales, Australia, having previously served as the Head of its Department of Applied Mathematics. He has written over 250 research papers in international journals and is the co-author of two monographs on Bäcklund transformations and their applications in continuum mechanics and soliton theory. He received his undergraduate degree from the University of Oxford and his DSc from the University of Nottingham, UK, for his published research in applied mathematics. He is a Fellow of the Australian Academy of Science, and was awarded its Hannan Medal for his major contributions in the detection of hidden invariance and symmetry properties in nonlinear mathematical systems descriptive of complex physical processes. He is a recipient of the Centennial Medal by the Australian Government.
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