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Solutions In Action
- 1st Edition - December 2, 2012
- Editor: Karl Lanngren
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 4 3 3 3 3 3 - 8
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 1 5 6 4 4 - 8
Solitons in Action is a collection of papers that discusses the concept of a wave packer or pulse known as a soliton. One paper reviews the development of the solitary wave… Read more
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Request a sales quoteSolitons in Action is a collection of papers that discusses the concept of a wave packer or pulse known as a soliton. One paper reviews the development of the solitary wave concept, with emphasis on the difference between a solitary wave and a soliton. The Korteweg-deVries (KdV) equation shows the interactions between infinite sets of conservation laws and the inverse scattering transform method. The Backlund transform technique produces hierarchies of multisoliton solutions for nonlinear wave equations. The Gel-'fand-Levitan algorithm can effect an inverse scattering calculation that relates changes in the scattering data to changes in the solution of corresponding wave equation. One paper points out that concepts in differential geometry can show the fundamental nature of soliton behavior and the relationship between inverse scattering and the Backlund transformation. Solitons in action can be viewed as magnetic flux propagates through a gap (between two closely-spaced superconductors) in quantum units. This view results in a simplified procedure for perturbation expansions around multisoliton solutions. This collection can prove useful for researchers involved in the study of fluid mechanics, of pure and applied sciences, of mathematical sciences, and of wave theory.
Contributors
Preface
An Introduction to Solitons and the Inverse Scattering Method via the Korteweg-deVries Equation
A Generalization of the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation and Application to the Korteweg-deVries Equation. A Variational Principle
Prolongations, Bäcklund Transformations, and Lie Theory as Algorithms for Solving and Understanding Nonlinear Differential Equations
Solitons and Physical Perturbations
Nonlinear Wave Concepts Applied to Deep-Water Waves
Observations of Solitons on Nonlinear Dispersive Transmission Lines
Experiments on Solitons in Plasmas
Fluxons in Long Josephson Junctions
A Multisoliton Perturbation Theory
Soliton Propagation in a One-Dimensional Lattice Under Shock Compresson
Stationary V-States
- No. of pages: 314
- Language: English
- Edition: 1
- Published: December 2, 2012
- Imprint: Academic Press
- Paperback ISBN: 9780124333338
- eBook ISBN: 9780323156448
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