Dynamics of Partial Differential Equations

Volume 13 (2016)

Number 1

Dedicated to emeritus associate editor Shiyi Chen

Asymptotic behavior of solutions to the cubic coupled Schrödinger systems in one space dimension

Pages: 53 – 74

DOI: http://dx.doi.org/10.4310/DPDE.2016.v13.n1.a3

Author

Victor V. Da Rocha (Laboratoire de Mathématiques Jean Leray, Université de Nantes, France)

Abstract

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.

Keywords

modified scattering, nonlinear Schrödinger equation

2010 Mathematics Subject Classification

35Q55

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Published 29 March 2016