Global Existence and Asymptotic Behavior of Solutions to Some Nonlinear Systems of Schrödinger Equations

J. Math. Sci. Univ. Tokyo
Vol. 22 (2015), No. 3, Page 771–792.

Nakamura, Yoshihisa ; Shimomura, Akihiro ; Tonegawa, Satoshi
Global Existence and Asymptotic Behavior of Solutions to Some Nonlinear Systems of Schrödinger Equations
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]


Abstract:
We study the global existence and the large time behavior of solutions to the coupled system of the Schrödinger equations with cubic nonlinearities in one space dimension. We construct modified wave operators to the system for small final data.

Keywords: Nonlinear Schrödinger equation, asymptotic behavior.

Mathematics Subject Classification (2010): 35Q55, 35B40.
Mathematical Reviews Number: MR3408074

Received: 2014-06-25