Conserved energies for the cubic NLS in 1-d
Abstract
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>-12 there exists a conserved energy which is equivalent to the Hs norm of the solution. For the Korteweg-de Vries (KdV) equation there is a similar conserved energy for every s -1.
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