Solutions In Action

Karl Lanngren

• Publisher: Academic Press
• Year: 2012
• Print ISBN: 9780124555808
• eBook ISBN: 9780323156448
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

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

• Front Cover
• Solitons in Action
• Copyright Page
• Table of Contents
• Dedication
• Contributors
• Preface
• Chapter 1. An Introduction to Solitons and the Inverse Scattering Method via the Korteweg– -deVries Equation
• Chapter 2. A Generalization of the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation and Application to the Korteweg-deVries Equation. A Variational Principle
• Chapter 3. Prolongations, Bäcklund Transformations, and Lie Theory as Algorithms for Solving and Understanding Nonlinear Differential Equations
• Chapter 4. Solitons and Physical Perturbations
• Chapter 5. Nonlinear Wave Concepts Applied to Deep-Water Waves
• Chapter 6. Observations of Solitons on Nonlinear Dispersive Transmission Lines
• Chapter 7. Experiments on Solitons in Plasmas
• Chapter 8. Fluxons in Long Josephson Junctions
• Chapter 9. A Multisoliton Perturbation Theory
• Chapter 10. Soliton Propagation in a One-Dimensional Lattice under Shock Compression
• Chapter 11. Stationary "V-States," Interactions, Recurrence, and Breaking
• Chapter 12. Biographical Notes on John Scott Russell
• Index