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Nonlinear Dispersive Waves

Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 1139503480
Size: 66.95 MB
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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.

The Water Waves Problem

Author: David Lannes
Publisher: American Mathematical Soc.
ISBN: 0821894706
Size: 79.70 MB
Format: PDF
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This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.

Nonlinear Waves In Solids

Author: A. Jeffrey
Publisher: Springer
ISBN: 3709124441
Size: 56.75 MB
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Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Beside fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up to date account of the current state of research in the theory and practice of nonlinear waves in solids.

Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions

Author: Thomas Trogdon
Publisher: SIAM
ISBN: 1611974194
Size: 28.44 MB
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Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.÷

Linear Elastic Waves

Author: John G. Harris
Publisher: Cambridge University Press
ISBN: 9780521643832
Size: 36.78 MB
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An advanced level textbook on wave propagation and scattering directed at applied mathematicians, seismologists, and engineers.

Solitons

Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521336550
Size: 26.61 MB
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This textbook is an introduction to the theory of solitons in the physical sciences.

Nonlinear Dispersive Equations

Author: Jaime Angulo Pava
Publisher: American Mathematical Soc.
ISBN: 0821848976
Size: 18.36 MB
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This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied includes Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.