Global Bifurcation of Spiral Wave Solutions to the Complex Ginzburg-Landau Equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912529530224640 |
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| author | Garcia-Azpeitia, Carlos Ghanem, Ziad Krawcewicz, Wieslaw |
| author_facet | Garcia-Azpeitia, Carlos Ghanem, Ziad Krawcewicz, Wieslaw |
| contents | We use the $\mathbb T^2$-equivariant degree to establish the existence of unbounded branches of rotating spiral wave solutions with any number of arms for the complex Ginzburg Landau equation GLe on the planar unit disc, leveraging the spatial symmetries inherent to the problem and avoiding limiting constraints encountered in previous studies (Dai 2021) that utilized the classical Leray-Schauder degree. Our results provide rigorous mathematical justification for the formation and persistence of these fundamental patterns, which are ubiquitous in physical, chemical, and biological systems but have, until now, eluded formal proof under general conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Bifurcation of Spiral Wave Solutions to the Complex Ginzburg-Landau Equation Garcia-Azpeitia, Carlos Ghanem, Ziad Krawcewicz, Wieslaw Analysis of PDEs We use the $\mathbb T^2$-equivariant degree to establish the existence of unbounded branches of rotating spiral wave solutions with any number of arms for the complex Ginzburg Landau equation GLe on the planar unit disc, leveraging the spatial symmetries inherent to the problem and avoiding limiting constraints encountered in previous studies (Dai 2021) that utilized the classical Leray-Schauder degree. Our results provide rigorous mathematical justification for the formation and persistence of these fundamental patterns, which are ubiquitous in physical, chemical, and biological systems but have, until now, eluded formal proof under general conditions. |
| title | Global Bifurcation of Spiral Wave Solutions to the Complex Ginzburg-Landau Equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.15098 |