Conserved energies for the cubic NLS in 1-d

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 $s>-\frac{1}{2}$ 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

References in corpus (1)

• Low regularity conservation laws for integrable PDE

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