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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 4
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Articles

Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation

Pages 801-825 | Received 16 Oct 2014, Accepted 19 Mar 2015, Published online: 07 Apr 2015
 

Abstract

This paper is concerned with a one-dimensional (1D) derivative nonlinear Schrödinger equation with periodic boundary conditions

We show that above equation admits a family of real analytic quasi-periodic solutions with two Diophantine frequencies and a family of real analytic periodic solutions. The proof is based on a partial Birkhoff normal form and KAM method.

AMS Subject Classifications:

Acknowledgements

The author thanks the editor and the referees for several kinds of suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the NNSF of China [11171185] and the NSF of Shandong Province [ZR2010AM013].

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