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| Author | : Eryk Infeld |
| Publisher | : Cambridge University Press |
| Total Pages | : 416 |
| Release | : 2000-07-13 |
| Genre | : Mathematics |
| ISBN | : 9780521635578 |
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
| Author | : G. Rowlands |
| Publisher | : |
| Total Pages | : 0 |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Stephen Nettel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 297 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 3662053179 |
This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
| Author | : J. Engelbrecht |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 197 |
| Release | : 2013-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 9401588910 |
At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
| Author | : Stephen Nettel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3662028255 |
This is a text for the third semester of undergraduate physics for students in accel erated programs who typicaHy are preparing for advanced degrees in science or engineering. The third semester is often the only opportunity for physics depart ments to present to those of these students who are not physics majors a coherent background in the physics of waves required later for confident handling of applied problems, especially applications based on quantum mechanics. Physics is an integrated subject. It is often found that the going gets easier as one goes deeper, learning the mathematical connections tying together the vari ous phenomena. Even so, the steps that took us from classical wave physics to Heisenberg's "Physical Principles of Quantum Theory" were, as a matter of his tory, harder to take than later steps dealing with detailed applications. With these considerations in mind, the classical physics of oscillations and waves is devel oped here at a more advanced mathematical level than is customary in second year courses. This is done to explain the classical phenomena, but also to provide background for the introductory wave mechanics, leading to a logical integration of the latter subject into the presentation. The concluding chapters on nonlinear waves, solitons, and chaos broaden the previously established concepts of wave behavior, while introducing the reader to important topics in current wave physics.
| Author | : Gérard A. Maugin |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780198534846 |
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
| Author | : Stephen Nettel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 289 |
| Release | : 2008-11-21 |
| Genre | : Science |
| ISBN | : 3540879080 |
This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
| Author | : |
| Publisher | : |
| Total Pages | : 114 |
| Release | : 1999 |
| Genre | : |
| ISBN | : |
| Author | : Anatoli? Mikha?lovich Kamchatnov |
| Publisher | : World Scientific |
| Total Pages | : 399 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 981024407X |
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.
| Author | : Mark J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 363 |
| Release | : 2011-09-08 |
| Genre | : Mathematics |
| ISBN | : 1139503480 |
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.
