“The Wave” “Par Excellence”, the Solitary Progressive Great Wave of Equilibrium of the Fluid: An Early History of the Solitary Wave

Abstract

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.