Nonlinear Resonance Analysis:Theory, Computation, Applications

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

Elena Kartashova is a Professor at the Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz. Her research interests include number theory, integrable dynamical systems, mathematical physics and their application in various areas, from fluid mechanics and meteorology to engineering. She was awarded the V.I. Vernadsky medal by the Russian Academy of Nutural Sciences in 2009