The story
Coined by Diederik Korteweg and Gustav de Vries in their paper in Philosophical Magazine (1895, series 5, vol. 39, pp. 422-443) to describe a class of solutions to the KdV equation which involve a Jacobi elliptic function. The Jacobi elliptic function involved is commonly written as cn(x|m), and the term cnoidal was designed to be analogous to sinusoidal, the word describing waves which involve the sine function.
Etymology from Wiktionary, CC BY-SA 4.0.