中国女人内谢25XXXX免费

讨论班 Seminar

【19.9.19 9:00-11:00】讨论班---钟学秀

2019-09-19 11:50:37 来源:讨论班---钟学秀 点击: 收藏本文

主讲人:钟学秀(华南数学应用与交叉中心)

时 间:2019年9月19日下午 9:00-11:00

地 点:华南数学应用与交叉研究中心学术课室114

题 目:The solutions of Nonlinear Schr\"odinger system


摘要:

Consider the following time-dependent system

\begin{equation}\label{system-t}

\left\{\begin{array}{l}{-i \frac{\partial}{\partial t} \Phi_{1}=\Delta \Phi_{1}+\mu_{1}\left|\Phi_{1}\right|^{2} \Phi_{1}+\beta\left|\Phi_{2}\right|^{2} \Phi_{1}, \quad x \in \Omega, t>0} \\ {-i \frac{\partial}{\partial t} \Phi_{2}=\Delta \Phi_{2}+\mu_{2}\left|\Phi_{2}\right|^{2} \Phi_{2}+\beta\left|\Phi_{1}\right|^{2} \Phi_{2}, \quad x \in \Omega, t>0} \\ {\Phi_{j}=\Phi_{j}(x, t) \in \mathbb{C}, \quad j=1,2} \\ {\Phi_{j}(x, t)=0, \quad x \in \partial \Omega, t>0, j=1,2}\end{array}\right.

\end{equation}

where $\Omega=\R^N$ or $\Omega\subset \R^N$ is a bounded smooth domain. $i$ is the imaginary unit,$\mu_1,\mu_2>0$ are constants. The ansatz $\Phi_1(x,t)=e^{i\lambda_1 t}u(x)$ and $\Phi_2(x,t)=e^{i\lambda_2t}v(x)$ for solitary wave solutions leads to the  elliptic system:

\begin{equation}\label{system}

\left\{\begin{array}{l}{-\Delta u+\lambda_{1} u=\mu_{1} u^{3}+\beta u v^{2}, \quad x \in \Omega} \\ {-\Delt