Introduction to the Mathematical Physics of Nonlinear Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Mathematical Physics of Nonlinear Waves write by Minoru Fujimoto. This book was released on 2014-03-01. Introduction to the Mathematical Physics of Nonlinear Waves available in PDF, EPUB and Kindle. Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
Nonlinear Optical Waves
Nonlinear Optical Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Optical Waves write by A.I. Maimistov. This book was released on 2013-03-09. Nonlinear Optical Waves available in PDF, EPUB and Kindle. A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.
Nonlinear Waves, Solitons and Chaos
Nonlinear Waves, Solitons and Chaos - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Waves, Solitons and Chaos write by Eryk Infeld. This book was released on 2000-07-13. Nonlinear Waves, Solitons and Chaos available in PDF, EPUB and Kindle. The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Nonlinear Periodic Waves and Their Modulations
Nonlinear Periodic Waves and Their Modulations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Periodic Waves and Their Modulations write by Anatoli? Mikha?lovich Kamchatnov. This book was released on 2000. Nonlinear Periodic Waves and Their Modulations available in PDF, EPUB and Kindle. 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.
Physics of Nonlinear Waves
Physics of Nonlinear Waves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Physics of Nonlinear Waves write by Mitsuhiro Tanaka. This book was released on 2019-12-18. Physics of Nonlinear Waves available in PDF, EPUB and Kindle. This is an introductory book about nonlinear waves. It focuses on two properties that various different wave phenomena have in common, the "nonlinearity" and "dispersion", and explains them in a style that is easy to understand for first-time students. Both of these properties have important effects on wave phenomena. Nonlinearity, for example, makes the wave lean forward and leads to wave breaking, or enables waves with different wavenumber and frequency to interact with each other and exchange their energies. Dispersion, for example, sorts irregular waves containing various wavelengths into gentler wavetrains with almost uniform wavelengths as they propagate, or cause a difference between the propagation speeds of the wave waveform and the wave energy. Many phenomena are introduced and explained using water waves as an example, but this is just a tool to make it easier to draw physical images. Most of the phenomena introduced in this book are common to all nonlinear and dispersive waves. This book focuses on understanding the physical aspects of wave phenomena, and requires very little mathematical knowledge. The necessary minimum knowledges about Fourier analysis, perturbation method, dimensional analysis, the governing equations of water waves, etc. are provided in the text and appendices, so even second- or third-year undergraduate students will be able to fully understand the contents of the book and enjoy the fan of nonlinear wave phenomena without relying on other books.
