Conserved energies for the cubic nonlinear Schrödinger equation in one dimension

Herbert Koch, Daniel Tataru

Type: Article

Publication Date: 2018-10-26

Citations: 53

DOI: https://doi.org/10.1215/00127094-2018-0033

Abstract

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>−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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