Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Inverse Scattering for the Korteweg-de Vries Equation
- 3 General Inverse Scattering in One Dimension
- 4 Inverse Scattering for Integro-Differential Equations
- 5 Inverse Scattering in Two Dimensions
- 6 Inverse Scattering in Multidimensions
- 7 The Painlevé Equations
- 8 Further Remarks and Open Problems
- Appendix A Remarks on Riemann-Hilbert problems
- Appendix B Remarks on ∂ problems
- References
- Subject Index
1 - Introduction
Published online by Cambridge University Press: 04 February 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Inverse Scattering for the Korteweg-de Vries Equation
- 3 General Inverse Scattering in One Dimension
- 4 Inverse Scattering for Integro-Differential Equations
- 5 Inverse Scattering in Two Dimensions
- 6 Inverse Scattering in Multidimensions
- 7 The Painlevé Equations
- 8 Further Remarks and Open Problems
- Appendix A Remarks on Riemann-Hilbert problems
- Appendix B Remarks on ∂ problems
- References
- Subject Index
Summary
Historical Remarks and Applications.
“Solitons” were first observed by J. Scott Russell in 1834 [1838, 1844] whilst riding on horseback beside the narrow Union canal near Edinburgh, Scotland. There are a number of discussions in the literature describing Russell's observations. Nevertheless we feel that his point of view is so insightful and relevant that we present it here as well. He described his observations as follows:
“I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped — not so the mass of water in the channel which it had put in motion; it accumulates round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and welldefined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that rare and beautiful phenomenon which I have called the Wave of Translation … .”
Subsequently, Russell did extensive experiments in a laboratory scale wave tank in order to study this phenomenon more carefully.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 1991
- 2
- Cited by