On the Existence and Stability of Standing Waves for 2-Coupled Nonlinear Fractional Schrödinger System. (27th December 2015)

• Record Type: Journal Article
• Authors: Sha, Xiuyan; Ge, Huanmin; Xin, Jie
• Other Names: Sivasundaram Seenith Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-12-27
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/427487
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We study a system of 2-coupled nonlinear fractional Schrödinger equations. Firstly, we construct constrained minimization problem to the system. Next, we prove the existence of standing waves for the system by using the concentration-compactness and commutator estimates method. Lastly, we also consider the set of minimizers of the constrained minimization problem. We prove that it is a stable set for initial value of the problem; that is, a solution to the system with initial value which is near the set will remain near it for all time.