Conserved energies for the cubic NLS in 1-d
arXiv:1607.02534 · doi:10.1215/00127094-2018-0033
Abstract
We consider the cubic Nonlinear Schrödinger 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 $s\ge -1$.
72 pages, small corrections