 KdV mass and energy conservation

ID: kdv-mass-and-energy-conservation

Sufficiently regular decaying solutions conserve

M (u) = \int_{R} u^{2}, E (u) = \frac{1}{2} \int_{R} u_{x}^{2} - \frac{1}{p + 1} \int_{R} u^{p + 1} .

Both identities follow by integration by parts from the divergence form of the equation.

 New to topics? Read the docs here!