Dynamics of Partial Differential Equations
Volume 13 (2016)
Dedicated to emeritus associate editor Shiyi Chen
Asymptotic behavior of solutions to the cubic coupled Schrödinger systems in one space dimension
Pages: 53 – 74
In this paper, we study a coupled nonlinear Schrödinger system with small initial data in the one dimension Euclidean space. Such a system appears in the context of the coupling between two different optical waveguides. We establish an asymptotic nonlinear behavior and a decay estimate for solutions of this system. The proof uses a recent work of Kato and Pusateri.
modified scattering, nonlinear Schrödinger equation
2010 Mathematics Subject Classification