Nonlinear Periodic Waves And Their Modulations: An Introductory Course
Regular price
€114.99
A01=Anatoly M Kamchatnov
Author_Anatoly M Kamchatnov
Category=PBWR
Category=PHDS
Dissipationless Shock Waves
eq_bestseller
eq_isMigrated=1
eq_nobargain
eq_non-fiction
eq_science
Hodograph Transform
Integrable Equations
Inverse Scattering Transform
Modulation
Modulational Instability
Nonlinear Waves
Periodic Solutions
Solitons
Whitham Theory
Product details
- ISBN 9789810244071
- Publication Date: 07 Sep 2000
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
