Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/90493
 Type: Artigo de periódico Title: A System Of Coupled Schrödinger Equations With Time-oscillating Nonlinearity Author: Carvajal X.Gamboa P.Panthee M. Abstract: This paper is concerned with the initial value problem (IVP) associated to the coupled system of supercritical nonlinear Schrödinger equations $$\left\{\begin{array}{@{}l@{}}iu-{t}+\Delta u+\theta-{1}(\omega t)(\vert u\vert{2p}+\beta \vert u\vert{p-1}\vert v \vert{p+1})u=0,\\ iv-{t}+\Delta v+\theta-2(\omega t)(\vert v \vert{2p}+\beta \vert v \vert{p-1}\vert u \vert{p+1})v=0,\end{array}\right.$$ where θ1 and θ2 are periodic functions, which has applications in many physical problems, especially in nonlinear optics. We prove that, for given initial data φ, ψ ⋯ H1(R n), as |ω| → ∞, the solution (uω, vω) of the above IVP converges to the solution (U, V) of the IVP associated to $$\left\{\begin{array}{@{}l@{}} iU-{t}+\Delta U+I(\theta-{1})(\vert U \vert{2p}+\beta \vert U \vert{p-1}\vert V \vert{p+1})U=0, \\[3pt] iV-{t}+\Delta V+I(\theta-{2})(\vert V \vert{2p}+\beta \vert V \vert{p-1}\vert U \vert{p+1})V=0, \end{array}\right.$$ with the same initial data, where I(g) is the average of the periodic function g. Moreover, if the solution (U, V) is global and bounded, then we prove that the solution (uω, vω) is also global provided |ω| ≫ 1. © 2012 World Scientific Publishing Company. Editor: Rights: fechado Identifier DOI: 10.1142/S0129167X12501194 Address: http://www.scopus.com/inward/record.url?eid=2-s2.0-84871331210&partnerID=40&md5=0f3e128872088e1d475afc37ee6c5552 Date Issue: 2012 Appears in Collections: Unicamp - Artigos e Outros Documentos

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