Journal of Applied Nonlinear Dynamics
Exact Analytical Solutions : Physical and/or Mathematical Validity
Journal of Applied Nonlinear Dynamics 10(1) (2021) 95109  DOI:10.5890/JAND.2021.03.006
P.H. KamdoumTamo$^{1,2}$ , E. TalaTebue$^{1,3}$, A.
KenfackJiotsa$^{1,2}$, 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, IUTFotso 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 GinzburgLandau 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 wellgrounded. The second type concerns new
solutions with infinite nonzero branches. For this second type,
direct numerical simulations are performed to show that they are
physically valid.
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