Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction

In this paper, we consider the asymptotic behavior of the ground state and its energy for the nonlinear Schrodinger system with three wave interaction on the parameter \begin{document}$ \gamma $\end{document} as \begin{document}$ \gamma \to \infty $\end{document} . In addition we prove the existence of the positive threshold \begin{document}$ \gamma^* $\end{document} such that the ground state is a scalar solution for \begin{document}$ 0 \le \gamma and is a vector solution for \begin{document}$ \gamma > \gamma^* $\end{document} .