On the development of the theory of the solitary wave. A historical essay

摘要: The mathematical evolution of the theory a solitary wave is followed from its inception when analytical mechanics was formed. Very early already, it recognized that motion differs water particles, but first exact solution theory, published by Gerstner in 1802, assumes both motions coincide. With Russell's experimental observations 1838, and with his classification waves into four orders, transmission, i.e. wave, solidly established as transfer momentum one spatial point to neighbour. His discovery permanent form, whose velocity depends on height started dispute. Several authors developed their own waves. most successful contributions were brought Airy 1845 nonlinear shallow non-permanent Stokes 1849 deep concluded holds whenever amplitude surface elevation relative depth smaller than ratio waterdepth wavelength:ηmax/h < (h/λ)2, whereas Airy's results implyηmax/h (h/λ)2 thus providing different physical phenomena. description form obtained Boussinesq 1871; rediscovered an other method Lord Rayleigh 1876. next steps improve stationary behaviour wave. had remarked pressure distribution at free not constant, invalidating stationarity solution. McCowan, 1894, Kortewegde Vries, 1895 gave more accurate for maximum possible waveheight. Later on, systematic expansions introduced allowed entire hierarchy be developed, process presently still being under way. In this context proofs convergence existence forementioned approximations irrotational perfect fluid are focus 20th century research.