| Abstract: |
| In this talk, we consider the following system of nonlinear
fractional Schr\{o}dinger equations with three wave interaction:
\begin{align}
\left\{
\begin{aligned}
(-\Delta)^{\alpha/2}u_1(x)+w_1u_1(x)-u_1^p(x)=\gamma u_2(x)u_3(x),x\in\mathbb{R}^n,\
(-\Delta)^{\alpha/2}u_2(x)+w_2u_2(x)-u_2^p(x)=\gamma u_1(x)u_3(x),x\in\mathbb{R}^n,\
(-\Delta)^{\alpha/2}u_3(x)+w_3u_3(x)-u_3^p(x)=\gamma
u_1(x)u_2(x),x\in\mathbb{R}^n.
\end{aligned}
\right.
\end{align}
By establishing the direct method of moving planes, we obtain radially symmetric and
monotone decreasing of positive solutions for this system. |
|