具有自诱导宇称时间对称势的可积非局部向量非线性薛定谔方程
Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
摘要：
研究了具有自诱导$ {\cal PT}$对称势的两分量非局域矢量非线性薛定谔方程（VNLSE）.证明了该系统具有一个拉克斯对和无穷多个守恒量，因而是可积的.一些守恒量，如数算符，哈密顿量等被发现是实值的，尽管这些费用是非厄米。利用逆散射变换的方法得到了该方程的孤子解，并给出了从非局域化为局域化的条件。一个非齐次版本的VNLSE与时空调制的非线性相互作用项也被认为是和映射的这个方程。与标准VNLSE通过相似性变换来生成其解。
英文摘要：
A two component nonlocal vector nonlinear Schrödinger equation (VNLSE) is considered with a self-induced $ {\cal PT}$ symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and hence integrable. Some of the conserved quantities like number operator, Hamiltonian etc. are found to be real-valued, in spite of these charges being non-hermitian. The soliton solution for the same equation is obtained through the method of inverse scattering transformation and the condition of reduction from nonlocal to local case is also mentioned. An inhomogeneous version of this VNLSE with space -time modulated nonlinear interaction term is also considered and a mapping of this Eq. with standard VNLSE through similarity transformation is used to generate its solutions.
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