Nonlinear waves [electronic resource] : a geometrical approach / Petar Popivanov, Angela Slavova.
By: Popivanov, Peter R
.
Contributor(s): Slavova, Angela.
Material type: 
Computer fileSeries: Series on analysis, applications, and computation ; v. 9.Publisher: Singapore : World Scientific Publishing Co. Pte Ltd., ©2018Description: 1 online resource (208 p.) : ill. (some col.).ISBN: 9789813271616.Subject(s): Nonlinear wave equations | Nonlinear waves | Mathematical physics | Nonlinear partial differential operators | Electronic booksDDC classification: 531/.113301515353 Online resources: Access to full text is restricted to subscribers. Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Title from web page (viewed December 5, 2018).
Includes bibliographical references and index.
Traveling waves and their profiles -- Solvability of PDEs from physics and geometry -- Interaction of peakons and kinks -- Dressing method and geometrical applications -- Hirota's method in soliton theory -- Special type solutions of evolution PDEs -- Regularity properties of nonlinear hyperbolic PDEs.
"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, quantum mechanics, amongst others."-- Publisher's website.
There are no comments for this item.