Exact Analytical Solutions : Physical and/or Mathematical Validity
DOI:
https://doi.org/10.5890/JAND.2021.03.006Abstract
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.References
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