nLab
Korteweg de Vries equation

Korteweg de Vries equation is a particular nonlinear wave equation:

$$u_t=(3u^2+u_{\mathrm{xx}}{)}_x$$u_t = (3u^2 + u_{xx})_x

It is one of the main examples in the study of integrable systems.

• M. Adler, On a trace functional for formal pseudo differential operators and the symplectic structure of the Korteweg de Vries type equations, Invent. Math. 50 (1978/79), no. 3, 219–248, MR520927