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arXiv · 1607.02534

Conserved energies for the cubic NLS in 1-d

Herbert Koch·Daniel Tataru
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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 $s>-\frac12$ 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 $s\ge -1$.

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Herbert Koch, Daniel Tataru. 2016-07-08. Conserved energies for the cubic NLS in 1-d. https://doi.org/10.1215/00127094-2018-0033

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