Nonlinear Waves: A Geometrical Approach (Analysis, Applications and Computation) - Hardcover

Popivanov, Petar Radoev; Slavova, Angela

Hardcover

ISBN 10: 9813271604 ISBN 13: 9789813271609

Publisher: World Scientific Publishing Company, 2019

Synopsis

This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2019
• Language: English
• ISBN 10: 9813271604
• ISBN 13: 9789813271609
• Binding: Hardcover
• Number of pages: 208