Invariant Measures for the DNLS Equation

Abstract

We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) constructed in [2, 3]. The construction works for small 2 data. The measures are absolutely continuous with respect to suitable weighted Gaussian measures supported on Sobolev spaces of increasing regularity. These results have been obtained in collaboration with Giuseppe Genovese