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Thomas J. Bridges - Symmetry, Phase Modulation and Nonlinear Waves, Inbunden

Inbunden, Engelska, 2017

Symmetry, Phase Modulation and Nonlinear Waves

Av Thomas J. Bridges

Del 31 i serien Cambridge Monographs on Applied and Computational Mathematics

1091 kr

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Beskrivning
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
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Thomas J. Bridges is currently Professor of Mathematics at the University of Surrey. He has been researching the theory of nonlinear waves for over 25 years. He is co-editor of the volume Lectures on the Theory of Water Waves (Cambridge, 2016) and he has over 140 published papers on such diverse topics as multisymplectic structures, Hamiltonian dynamics, ocean wave energy harvesting, geometric numerical integration, stability of nonlinear waves, the geometry of the Hopf bundle, theory of water waves and phase modulation.

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'This book has been written by a well-established researcher in the field. His expertise is evidenced by the deft exposition of relatively challenging material. In that regard, one of the very useful functions of this book is its provision of a number of background mathematical techniques in Hamiltonians systems, symplectic geometry, Noether theory and Lagrangian field theory.' K. Alan Shore, Contemporary Physics

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