KORTEWEG, D.J. & G. DE VRIES - THE KORTEWEG-DE VRIES EQUATION FOR THE SOLITARY WAVE

On the Change of Form of Long Waves advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves.

London,Taylor and Francis, 1895. 8vo. Contemp. hcalf. Gilt lettering to spine. A stamp at foot of titlepage. In: No wrappers. In: "The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science", Vol. XXXIX, Fifth Series. VI,(1),552 pp. a. 7 plates. The paper: pp. 422-443. Internally clean and fine.

First appearance of the paper in which the authors set forth the equation which bears their name.The equation is named for Diederik Korteweg and Gustav de Vries who studied it, though the equation first appears in Boussinesqs work, 1877.

"In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium.... Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described by John Scott Russell (1808-1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".

Scott Russell's experimental work seemed at odds with Isaac Newton's and Daniel Bernoulli's theories of hydrodynamics. George Biddell Airy and George Gabriel Stokes had difficulty accepting Scott Russell's experimental observations because they could not be explained by the existing water wave theories. Their contemporaries spent some time attempting to extend the theory but it would take until the 1870s before Joseph Boussinesq and Lord Rayleigh published a theoretical treatment and solutions. In 1895 Diederik Korteweg and Gustav de Vries provided what is now known as the Korteweg-de Vries equation, including solitary wave and periodic cnoidal wave solutions." (Wikipedia).

Order-nr.: 47026