Author:
Kurata Kazuhiro,Osada Yuki
Abstract
<p style='text-indent:20px;'>In this paper, we consider the asymptotic behavior of the ground state and its energy for the nonlinear Schrödinger system with three wave interaction on the parameter <inline-formula><tex-math id="M1">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M2">\begin{document}$ \gamma \to \infty $\end{document}</tex-math></inline-formula>. In addition we prove the existence of the positive threshold <inline-formula><tex-math id="M3">\begin{document}$ \gamma^* $\end{document}</tex-math></inline-formula> such that the ground state is a scalar solution for <inline-formula><tex-math id="M4">\begin{document}$ 0 \le \gamma < \gamma^* $\end{document}</tex-math></inline-formula> and is a vector solution for <inline-formula><tex-math id="M5">\begin{document}$ \gamma > \gamma^* $\end{document}</tex-math></inline-formula>.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Analysis,General Medicine
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