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Journal of Applied Nonlinear Dynamics 10(1) (2021) 95--109 | DOI:10.5890/JAND.2021.03.006

P.H. Kamdoum-Tamo$^{1,2}$ , E. Tala-Tebue$^{1,3}$, A. Kenfack-Jiotsa$^{1,2}$, T.C. Kofane$^{1}$

$^{1}$ Laboratory of Mechanics, Department of Physics, Faculty of Sciences, and African Center of Excellence in I.C.T (C.E.T.I.C) University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

$^{2}$ Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers Training College, University of Yaounde I, P.O. Box 47 Yaounde, Cameroon

$^{3}$ Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

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Abstract

In this work, we use the alternative ($G'/G$)-expansion method, the sech method, the tanh method and the Painleve truncated approach to find solutions of the modified complex Ginzburg-Landau equation. We show that any mathematically acceptable solution is not necessarily physically suitable. Among the two types of obtained solutions, there is a category with null infinite branches, for which no direct numerical simulation can be carried out. This type of solutions is however mathematically well-grounded. The second type concerns new solutions with infinite non-zero branches. For this second type, direct numerical simulations are performed to show that they are physically valid.

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