Nonlinear Waves: A Geometrical Approach
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A01=Angela Slavova
A01=Petar Radoev Popivanov
Author_Angela Slavova
Author_Petar Radoev Popivanov
Category=PBKJ
Category=PHU
Dressing Method and Hirota's Direct Method in Studying Nonlinear Waves
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Evolution PDEs
Exact Solutions
Geometrical Visualization of Nonlinear Waves
Interaction of Waves
Kinks
Loops
Method of the Simplest Equation
Nonlinear Waves
Ovals and Peakon Types
Partial Differential Equations in Mathematical Physics
Propagation of Waves and New Born Waves
Rational Solutions
Regularizing Properties of the Solutions of Dissipative Semilinear PDEs
Rogue Waves
Solitons
Traveling Waves
Wave Front Sets of the Solutions of Nonlinear Systems of PDEs
Product details
- ISBN 9789813271609
- Publication Date: 09 Jan 2019
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
