Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
Open Access Publications from the University of California

## Conserved energies for the cubic nonlinear Schrödinger equation in one dimension

• Author(s): Koch, Herbert
• Tataru, Daniel
• et al.

## Published Web Location

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