Nonlinear Dispersive Waves and Fluids

Nonlinear Dispersive Waves and Fluids
Title Nonlinear Dispersive Waves and Fluids PDF eBook
Author Avy Soffer
Publisher American Mathematical Soc.
Pages 290
Release 2019-03-12
Genre Mathematics
ISBN 1470441098

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This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics. The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.

Ray Methods for Nonlinear Waves in Fluids and Plasmas

Ray Methods for Nonlinear Waves in Fluids and Plasmas
Title Ray Methods for Nonlinear Waves in Fluids and Plasmas PDF eBook
Author Marcelo Anile
Publisher CRC Press
Pages 268
Release 2021-06-24
Genre Mathematics
ISBN 1000447588

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Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

Nonlinear Dispersive Waves

Nonlinear Dispersive Waves
Title Nonlinear Dispersive Waves PDF eBook
Author David Henry
Publisher Springer Nature
Pages 288
Release
Genre
ISBN 3031635124

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Nonlinear Dispersive Waves

Nonlinear Dispersive Waves
Title Nonlinear Dispersive Waves PDF eBook
Author Mark J. Ablowitz
Publisher Cambridge University Press
Pages 363
Release 2011-09-08
Genre Mathematics
ISBN 1139503480

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The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Linear and Nonlinear Waves

Linear and Nonlinear Waves
Title Linear and Nonlinear Waves PDF eBook
Author G. B. Whitham
Publisher John Wiley & Sons
Pages 660
Release 2011-10-18
Genre Science
ISBN 1118031202

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Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Nonlinear Dynamics

Nonlinear Dynamics
Title Nonlinear Dynamics PDF eBook
Author Muthusamy Lakshmanan
Publisher Springer Science & Business Media
Pages 628
Release 2012-12-06
Genre Mathematics
ISBN 3642556884

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This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Nonlinear Periodic Waves and Their Modulations

Nonlinear Periodic Waves and Their Modulations
Title Nonlinear Periodic Waves and Their Modulations PDF eBook
Author Anatoli? Mikha?lovich Kamchatnov
Publisher World Scientific
Pages 399
Release 2000
Genre Science
ISBN 981024407X

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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.