Abstract
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.
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