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Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
Published Web Location
https://doi.org/10.1215/00127094-2018-0033Abstract
We consider the cubic nonlinear Schrödinger (NLS) equation as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension. We prove that for each s > -1/2 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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