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A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.

Solitons. --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of

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Kinks and domain walls are the simplest kind of solitons and are invaluable for testing various ideas and for learning about non-perturbative aspects of field theories. They are the subject of research in essentially every branch of physics, ranging from condensed matter to cosmology. This book is an introduction to kinks and domain walls and their principal classical and quantum properties. The book examines classical solitons, building from examples in elementary systems to more complicated settings. The formation of solitons in phase transitions, their dynamics and their cosmological consequences are further discussed. The book closes with an explicit description of a few laboratory systems containing solitons. Kinks and Domain Walls includes several state-of-the-art results, some previously unpublished. Each chapter closes with open questions and research problems and will be of great interest to both graduate students and academic researchers in theoretical physics, particle physics, cosmology and condensed matter physics.

Solitons. --- Connections (Mathematics) --- Geometry, Differential --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Nonlinear theories --- Wave-motion, Theory of

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When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and K

Mathematical physics. --- Solitons --- Mathematics. --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Physical mathematics --- Physics --- Mathematics

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In this work, the fundamentals of physics of solitons are presented using examples from macroscopic physics. The main theoretical methods are first shown, followed by a detailed presentation of numerous applications dedicated to the microscopic problems of the physics of solids or biological macromolecules.

Solitons. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of

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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 developme

Nonlinear waves. --- Wave-motion, Theory of. --- Solitons. --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Waves --- Undulatory theory --- Mechanics