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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.
Rights: fechado
Identifier DOI: 10.1142/S0129167X12501194
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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