S ep 2 00 0 AN ADDITIONAL GIBBS ’ STATE FOR THE CUBIC SCHRÖDINGER EQUATION ON THE CIRCLE

@inproceedings{Vaninsky2008SE2,
  title={S ep 2 00 0 AN ADDITIONAL GIBBS ’ STATE FOR THE CUBIC SCHR{\"O}DINGER EQUATION ON THE CIRCLE},
  author={K. L. Vaninsky},
  year={2008}
}
  • K. L. Vaninsky
  • Published 2008
Abstract. An invariant Gibbs’ state for the nonlinear Schrödinger equation on the circle was constructed by Bourgain, [B], and McKean, [MC], out of the basic Hamiltonian using a trigonometric cut-off. The cubic nonlinear Schrödinger equation is a completely integrable system having an infinite number of additional integrals of motion. In this paper we construct the second invariant Gibbs’ state from one of these additional integrals for the cubic NLS on the circle. This additional Gibbs’ state… CONTINUE READING

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