Symmetry, Phase Modulation and Nonlinear Waves: Series Number 31 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 31) - Hardcover

Bridges, Thomas J.

Hardcover

ISBN 10: 1107188849 ISBN 13: 9781107188846

Publisher: Cambridge University Press, 2017

Synopsis

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.

About this title

About the Author

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2017
• Language: English
• ISBN 10: 1107188849
• ISBN 13: 9781107188846
• Binding: Hardcover
• Edition number: 1
• Number of pages: 236