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Lorentzian-type soliton solutions of ac-driven complex Ginzburg-Landau equation. (English) Zbl 1290.35258

The authors studied the fractional transform solutions of the modified one-dimensional complex Ginzburg-Landau equation with a ac-driver. They aimed to find exact Lorentzian-type solutions for the equation by using an ansatz involving the difference between the solution and the external driver. Then, for certain choices of external phase and amplitude, the authors gave solution formulas for the resulting second-order differential equation. This part is followed by a numerical study of the trigonometric solutions. White noise and some perturbations were introduced to the solutions, and the numerical simulations indicate that the solutions are quite stable in presence of small perturbations.

MSC:

35Q56 Ginzburg-Landau equations
35Q51 Soliton equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35C09 Trigonometric solutions to PDEs
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