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Periodic solutions of the Ginzburg-Landau equation |
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| Affiliation: | 1. Mathematics Department, Faculty of Science, Taibah University, Saudi Arabia;2. Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt;3. Department of Mathematics, Institute of Applied Sciences & Humanities, GLA University, Mathura 281406, Uttar Pradesh, India |
| Abstract: | Spatially periodic solutions to the Ginzburg-Landau equation are considered. In particular we obtain: criteria for primary and secondary bifurcation; limit cycle solutions; nonlinear dispersion relations relating spatial and temporal frequencies. Only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered. Finally we briefly treat the case of spatial bifurcations. |
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