01778nmm a2200265 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001000139100002300149245009300172260004800265300002700313653002900340653002000369653002100389041001900410989003200429490006600461856006000527082002000587520090500607EB001528050EBX0100000000000000092613600000000000000.0cr|||||||||||||||||||||170706 ||| eng a9781316986769 4aQA9271 aBridges, Thomas J.00aSymmetry, phase modulation, and nonlinear wavescThomas J. Bridges, University of Surrey aCambridgebCambridge University Pressc2017 aix, 228 pagesbdigital aNonlinear wave equations aNonlinear waves aPhase modulation07aeng2ISO 639-2 bCBOaCambridge Books Online0 aCambridge monographs on applied and computational mathematics uhttps://doi.org/10.1017/9781316986769xVerlag3Volltext0 a531.11330151535 aNonlinear 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