TY  - BOOK
AU  - Bridges,Thomas J.
TI  - Symmetry, phase modulation, and nonlinear waves
T2  - Cambridge monographs on applied and computational mathematics
SN  - 9781107188846
AV  - QA927 .B75 2017
U1  - 531.11330 BRI-T 23
PY  - 2017///
CY  - UK
PB  - Cambridge
KW  - Nonlinear wave equations
KW  - Nonlinear waves
KW  - Phase modulation
N1  - 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; Includes bibliographical references and index
ER  -