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- W2020531293 abstract "This paper examines the bifurcation and stability of the solutionsof the complex Ginzburg--Landau equation(CGLE). The structure of thebifurcated solutions shall be explored as well. We investigate twodifferent modes of the CGLE. The first mode of the CGLE containsonly an unstable cubic term and the second mode contains not only acubic term but a quintic term. The solutions of the cubic CGLEbifurcate from the trivial solution to an attractor supercriticallyin some parameter range. However, for the cubic-quintic CGLE, asubcritical bifurcation is obtained. Due to the global attractor, weobtain a saddle node bifurcation point $lambda_c$. By thoroughlyinvestigating the structure and transition of the solutions of theCGLE, we confirm that the bifurcated solutions are homeomorphic to$S^1$ and contain steady state solutions." @default.
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- W2020531293 date "2008-01-01" @default.
- W2020531293 modified "2023-09-25" @default.
- W2020531293 title "Bifurcation and stability of the generalized complex Ginzburg--Landau equation" @default.
- W2020531293 doi "https://doi.org/10.3934/cpaa.2008.7.1237" @default.
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