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“The Wave” “Par Excellence”, the solitary progressive great wave of equilibrium of the fluid: An early history of the solitary wave. (English) Zbl 0644.76018

Solitons, Proc. Winter Sch., Tiruchirapalli/India 1987, Springer Ser. Nonlinear Dyn., 7-42 (1988).
[For the entire collection see Zbl 0638.00017.]
It is shown how in 1876 Rayleigh resolved the conflict between Russell on the one hand, and Stokes and Airy on the other, about the nature of the solitary wave and the formula for its velocity of propagation c. However, Boussinesq had already done this in 1872 when he published the Boussinesq equation and gave its solitary wave solution. The fundamental articles by Russell of 1840 and 1844 which first introduced the solitary wave and gave the formula \(c=\sqrt{g(h+k)}\) for its velocity are surveyed. They show that he understood the collision properties of solitons in 1835, though these objects and their mathematics emerged only some 130 years later.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
01A55 History of mathematics in the 19th century

Citations:

Zbl 0638.00017