Solutions In Action - 1st Edition - ISBN: 9780124555808, 9780323156448

Solutions In Action

1st Edition

Editors: Karl Lanngren
eBook ISBN: 9780323156448
Imprint: Academic Press
Published Date: 28th January 1978
Page Count: 314
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Description

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 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.

Table of Contents


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

Details

No. of pages:
314
Language:
English
Copyright:
© Academic Press 1978
Published:
Imprint:
Academic Press
eBook ISBN:
9780323156448

About the Editor

Karl Lanngren