ABSTRACT
We prove the long time orbital stability of the plane wave solutions to the nonlinear Schrödinger equation (NLS) in the defocusing () or focusing () case, More precisely, in a Gevrey space for some positive constant σ, we show that solution with the initial datum in the -neighborhood of the plane wave solution still stays in the -neighborhood ( C>4 ) of the plane wave solution for a subexponential long time where and .
2000 Mathematics Subject Classifications:
Acknowledgments
The authors are very grateful to Professor Hongzi Cong for his helpful suggestions and the helpful discussions.
Disclosure statement
No potential conflict of interest was reported by the authors.