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 3 (1978/79) 219–248 [MR520927]

History and relation to the hadrodynamics of quarkonium:

• Chris Quigg: From the Great Wave of Translation to the Force between Quarks [arXiv:2606.24052]