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Type: Artigo
Title: Scattering for a 3D coupled nonlinear Schrodinger system
Author: Farah, Luiz Gustavo
Pastor, Ademir
Abstract: We consider a three-dimensional coupled cubic nonlinear Schrödinger system appearing in nonlinear optics. If (P, Q) is a ground state solution, we show that for any initial data (u(0), v(0)) in H-1 (R-3) x H-1 (R-3) satisfying M (u(0), v(0))Lambda(u(0), v(0)) < M (P, Q)Lambda(P, Q) and M(u(0), v(0))E(u(0), v(0)) < M (P, Q)E(P, Q), where M(u, v) and E(u, v) are the mass and energy (invariant quantities) associated with the system, the corresponding solution is global in H-1(R-3) x H-1(R-3) and scatters. Our approach is in the same spirit of Duyckaerts, Holmer, and Roudenko [Math. Res. Lett. 15, 1233-1250 (2008)], where the authors considered the 3D cubic nonlinear Schrödinger equation
Subject: Schrödinger
Equação não-linear de
Sistemas não-lineares
Problema de
Non-linear Schrodinger equation
Nonlinear systems
Cauchy problem
Country: Estados Unidos
Editor: AIP Publishing
Rights: fechado
Identifier DOI: 10.1063/1.4993224
Date Issue: 2017
Appears in Collections:IMECC - Artigos e Outros Documentos

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