KdV mass and energy conservation
= KdV mass and energy conservation
{c}
Sufficiently regular decaying solutions conserve
$$
M(u)=\int_{\mathbb R}u^2,
\qquad
E(u)=\frac12\int_{\mathbb R}u_x^2-
\frac1{p+1}\int_{\mathbb R}u^{p+1}.
$$
Both identities follow by <integration by parts> from the divergence form of the equation.
= KdV mass conservation
{synonym}
= KdV energy conservation
{synonym}