  We consider the cubic Nonlinear Schr\"odinger Equation (NLS) as well as the
modified Korteweg-de Vries (mKdV) equation in one space dimension. We prove
that for each $s>-\frac12$ there exists a conserved energy which is equivalent
to the $H^s$ norm of the solution. For the Korteweg-de Vries (KdV) equation
there is a similar conserved energy for every $s\ge -1$.
