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

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