Author:
Chang Yonghang,Liao Menglan
Abstract
<abstract><p>In this paper, the Cauchy problem for the nonlinear Schrödinger system</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} i\partial_tu_1(x, t) = \Delta u_1(x, t)-|u_1(x, t)|^{p-1}u_1(x, t)-|u_2(x, t)|^{p-1}u_1(x, t), \\ i\partial_tu_2(x, t) = \Delta u_2(x, t)-|u_2(x, t)|^{p-1}u_2(x, t)-|u_1(x, t)|^{p-1}u_2(x, t), \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p>
<p>was investigated in $ d $ space dimensions. For $ 1 < p\le 1+2/d $, the nonexistence of asymptotically free solutions for the nonlinear Schrödinger system was proved based on mathematical analysis and scattering theory methods. The novelty of this paper was to give the proof of pseudo-conformal identity on the nonlinear Schrödinger system. The present results improved and complemented these of Bisognin, Sepúlveda, and Vera(Appl. Numer. Math. <bold>59</bold>(9)(2009): 2285–2302), in which they only proved the nonexistence of asymptotically free solutions when $ d = 1, \; p = 3 $.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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