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Type: Artigo de periódico
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 Schrodinger equations {iu(t) + Delta u + theta(1)(omega t)(vertical bar u vertical bar(2p) + beta vertical bar u vertical bar(p-1)vertical bar upsilon vertical bar(p+1))u = 0, iv(t) + Delta v + theta(2)(omega t)(vertical bar v vertical bar(2p) + beta|v|(p-1)vertical bar u vertical bar(p+1)) v = 0, where theta(1) and theta(2) are periodic functions, which has applications in many physical problems, especially in nonlinear optics. We prove that, for given initial data phi, psi is an element of H-1(R-n), as vertical bar omega vertical bar -> 8, the solution (u(omega), v(omega)) of the above IVP converges to the solution (U, V) of the IVP associated to {iU(t) + Delta U + I(theta(1))(vertical bar U vertical bar(2p) + beta vertical bar U vertical bar(p-1)vertical bar V vertical bar(p+ 1)) U = 0, iV(t) + Delta V + I(theta(2))(vertical bar V vertical bar(2p) + beta vertical bar V vertical bar(p-1)vertical bar U vertical bar(p+ 1)) V = 0, 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 (u., v.) is also global provided vertical bar omega vertical bar >> 1.
Subject: Schrodinger equation
initial value problem
Strichartz estimate
Country: Singapura
Editor: World Scientific Publ Co Pte Ltd
Rights: fechado
Identifier DOI: 10.1142/S0129167X12501194
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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