Abstract
In this paper, we analyze the complex Ginzburg-Landau equation with law of four powers of nonlinearity by using the complete discrimination system for polynomial method and establish the exact solutions of this equation. As the model is visualised under specific parameters, we give two-dimensional diagrams of the exact solutions to demonstrate the existence of the solutions. In addition, we also establish the dynamic properties of the equation and give the Hamiltonian and topological properties of the equation.
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