Abstract The complex Ginzburg-Landau equation is considered using the traveling wave reduction. The first integral for the system of nonlinear differential equations is found. The first integrals is used to reduce the system of equations to the second-order ordinary differential equation. The general solutions for the five constraints on the parameters of the original complex Ginzburg-Landau equation are given. All these solutions are expressed via the Weierstrass and the Jacobi elliptic functions.

中文翻译：

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复Ginzburg-Landau方程的一阶积分及通解

摘要 使用行波约简考虑了复Ginzburg-Landau方程。找到非线性微分方程组的第一个积分。一阶积分用于将方程组化简为二阶常微分方程。给出了原复Ginzburg-Landau方程参数的五个约束的通解。所有这些解都通过 Weierstrass 和 Jacobi 椭圆函数表示。