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Report on Waves, made to the meetings of the British Association in 1842-43.London: Richard and John E. Taylor, 1845.
First edition, extremely rare separately-paginated offprint issue (two copies in OCLC) of this classic paper describing Russell's discovery of 'solitary waves,' now known as 'solitons.'

In 1834, while conducting experiments to determine the most efficient design for canal boats, he discovered a phenomenon that he described as the 'wave of translation,' now known as a 'solitary wave': "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 accumulated 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 well-defined 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 singular and beautiful phenomenon which I have called the Wave of Translation" (p. 13).

Russell built wave tanks at his home to carry out experiments and noticed some key properties of solitary waves: they are stable, and can travel over very large distances; their speed depends on the size of the waves, and their width on the depth of water; unlike normal waves they will never merge-so a small wave is overtaken by a large one, rather than the two combining. These observations did not fit the existing theories of fluid dynamics, and it was not until the 1870s that the first full theoretical treatment of Russell's wave of translation was published by Joseph Boussinesq and Lord Rayleigh. The first mathematical model of waves on shallow water surfaces was published much later, in 1895, by Diederik Korteweg and Gustav de Vries. What is now known as the Korteweg-de Vries equation is the prototypical textbook nonlinear partial differential equation whose solutions can be exactly and unambiguously found; solitons constitute one of its families of solutions.

Russell was convinced that his wave of translation would one day be considered of fundamental importance, but it was not until the 1960s and the advent of modern computers that the significance of his discovery in physics, electronics, and biology started to become understood. Solitons appear in the description of many optical phenomena that involve nonlinear crystals (where the optical properties of the crystal do not respond linearly to the electric field of the incoming light), as well as in fibre optics, where the intrinsic stability of solitons is crucial when designing optical fibres for long-distance transmission. As the same mathematical models describe a wide range of physical systems, solitons also appear in the treatment of phenomena as diverse as shock waves and plasma, low-frequency oscillations in complex chemical structures such as DNA, and fluid dynamics.

Solitons are a recurring trait in the family tree of nonlinear differential equations. They also occur among the families of solutions of other equations that are directly related to, or nonlinear generalizations of, equations that shaped our understanding of the quantum world. In particular, the Schrödinger equation, which describes the time evolution of the quantum state associated with a physical system, has a nonlinear version which has soliton solutions, and which appear in the analysis of the interactions of some classes of subatomic particles. The nonlinear Schrödinger equation can also help describe rogue waves: unusually large spontaneous ocean surface waves that represent a threat even to ocean liners and super-tankers.. Offprint from the Report of the British Association for the Advancement of Science for 1844. Large 4to (), pp. 88 and 11 plates (one folding). Contemporary half-morocco, ruled and lettered in gilt, marbled edges and matching endpapers, a fine copy

      [Bookseller: Sophia Rare Books]
Last Found On: 2014-10-02           Check availability:      Antikvariat    

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