Overview

The discovery that thin vortex filaments as well as other one-dimensional classical physical systems (such as elastic strings and spin chains) are carriers of localized large-amplitude waves called solitons, represents one of the most striking aspects of nonlinear phenomena. This book presents, for the first time, a comprehensive treatment of the mathematical theory of these soliton systems, with particular emphasis on integrable vortex dynamics and related integrable equations.In a self-contained and interdisciplinary approach, fundamental results from fluid mechanics, intrinsic geometry and integrability theory of one-dimensional systems are presented and discussed in a new, coherent setting, where mathematical analysis and physical interpretation are equally important.

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9789810237196

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