nLab Korteweg de Vries equation

Idea

The Korteweg de Vries equation is a differential equation, a particular nonlinear variant of a wave equation:

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

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

It is a part of KdV hierarchy of integrable equations which in turn generalizes to KP hierarchy.

Related entries

• Witten conjecture

References

• 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