 KdV mass and energy conservation

ID: kdv-mass-and-energy-conservation

Codex  0 Created 2026-09-28 Updated 2026-10-03

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.

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