On invariant Gibbs measures for the generalized KdV equations

Tadahiro Oh, Geordie Richards, Laurent Thomann

Research output: Contribution to journalArticlepeer-review


We consider the generalized KdV equations on the circle. In particular, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure. In handling a nonlinearity of an arbitrary high degree, we make use of the Hermite polynomials and the white noise functional.
Original languageEnglish
Pages (from-to)133-153
Number of pages21
JournalDynamics of Partial Differential Equations
Volume 13
Issue number2
Publication statusPublished - 23 Jun 2016


  • generalized KdV equation
  • Gibbs measure
  • Hermite polynomial
  • white noise functional


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