Conserved energies for the cubic NLS in 1-d

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>-12 there exists a conserved energy which is equivalent to the Hs norm of the solution. For the Korteweg-de Vries (KdV) equation there is a similar conserved energy for every s -1.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…