Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
- Author(s): Koch, Herbert
- Tataru, Daniel
- et al.
Published Web Locationhttps://doi.org/10.1215/00127094-2018-0033
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 $s\ge -1$.