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摘要
This paper is concerned with the initial value problem (IVP) associated to the coupled system of supercritical nonlinear Schrodinger equations %26lt;br%26gt;{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, %26lt;br%26gt;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 -%26gt; 8, the solution (u(omega), v(omega)) of the above IVP converges to the solution (U, V) of the IVP associated to %26lt;br%26gt;{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, %26lt;br%26gt;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 %26gt;%26gt; 1.
- 出版日期2012-11
