We classify the Lie point symmetries of a system of nonlinearly coupled complex Ginzburg–Landau equations with time and space dependent potentials and nonlinearities. New families of systems with exact solutions and conservation laws are identified. When there is only space dependence, the system can be reduced to a set of ordinary differential equations for the amplitude and phase components, for which integrability and first integrals are discussed.

中文翻译：

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具有可变系数的两成分复金茨堡-朗道系统的李对称性

我们对具有时间和空间相关势和非线性的非线性耦合复Ginzburg-Landau方程组的系统的Lie点对称性进行分类。确定了具有精确解决方案和保护法则的新系统系列。当仅存在空间依赖性时，可以将系统简化为一组振幅和相位分量的常微分方程，并讨论其可积性和第一积分。