Abstract
The complex Ginzburg-Landau equation with anti-cubic nonlinearity is considered. Using a modification of the simplest equation method for finding exact solutions of nonlinear partial differential equations we get new solitary waves with arbitrary amplitude and speed of this special case of the complex Ginzburg -Landau equation. The first integral of nonlinear ordinary differential equation is found. The general solution of equation is presented taking into account the first integral of equation. Conserved density of the solitary wave solution is calculated.
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