English: Numerical solution of the KdV equation ut + uux + δ2uxxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Its calculation was done by the Zabusky-Kruskal scheme reported in the reference. The initial cosine wave evolves into a train of solitary-type waves.
Reference
N.J. Zabusky and M. D. Kruskal, Phy. Rev. Lett., 15, 240 (1965)