利用非幺正变换构造具有平衡损失和增益的向量非线性薛定谔方程的可解模型
Constructing Solvable Models of Vector Non-linear Schrodinger Equation with Balanced Loss and Gain via Non-unitary transformation
摘要：
本文研究了具有平衡增益损耗（BLG）、线性耦合（LC）和一般形式的立方非线性项的矢量非线性薛定谔方程（NLSE）。我们使用一个非幺正变换表明，该系统可以精确地映射到相同的方程没有BLG和LC，并与修改的时间调制的非线性相互作用。非线性项保持不变，而BLG和LC被完全删除，为一个特殊的情况下的伪酉变换。该映射是通用的，可以用来构造完全可解的自治以及非自治向量NLSE与BLG。我们提出了一个精确可解的具有幂振荡的BLG的二分量向量NLSE。最后给出了一个具有BLG和任意偶数个分量的矢量NLSE的例子。
英文摘要：
We consider vector Non-linear Schrodinger Equation(NLSE) with balanced loss-gain(BLG), linear coupling(LC) and a general form of cubic nonlinearity. We use a non-unitary transformation to show that the system can be exactly mapped to the same equation without the BLG and LC, and with a modified time-modulated nonlinear interaction. The nonlinear term remains invariant, while BLG and LC are removed completely, for the special case of a pseudo-unitary transformation. The mapping is generic and may be used to construct exactly solvable autonomous as well as non-autonomous vector NLSE with BLG. We present an exactly solvable two-component vector NLSE with BLG which exhibits power-oscillation. An example of a vector NLSE with BLG and arbitrary even number of components is also presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
