The cubic Schrödinger equation is considered on the circle, both in the de-focussing and the focussing case. The existence of the flow is proved together with the invariance of the appropriate Gibbsian measure, namely the petit canonical measure in the defocussing case and the micro-canonical measure in the focussing case.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics