Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy
The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3×3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients. Based on the characteristic polynomial of the Lax matrix for the CCIRD hierarchy, we introduce a trigonal curve Km−2 of arith...
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6618932 |
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| author | Chao Yue Tiecheng Xia |
| author_facet | Chao Yue Tiecheng Xia |
| author_sort | Chao Yue |
| collection | DOAJ |
| description | The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3×3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients. Based on the characteristic polynomial of the Lax matrix for the CCIRD hierarchy, we introduce a trigonal curve Km−2 of arithmetic genus m−2, from which the corresponding Baker-Akhiezer function and meromorphic functions on Km−2 are constructed. Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. In particular, algebro-geometric solutions for the entire CCIRD hierarchy are obtained. |
| format | Article |
| id | doaj-art-9d11322de45848ca97e03ca55f6c7e50 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-9d11322de45848ca97e03ca55f6c7e502025-02-03T01:25:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66189326618932Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion HierarchyChao Yue0Tiecheng Xia1College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian 271000, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaThe coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3×3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients. Based on the characteristic polynomial of the Lax matrix for the CCIRD hierarchy, we introduce a trigonal curve Km−2 of arithmetic genus m−2, from which the corresponding Baker-Akhiezer function and meromorphic functions on Km−2 are constructed. Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. In particular, algebro-geometric solutions for the entire CCIRD hierarchy are obtained.http://dx.doi.org/10.1155/2021/6618932 |
| spellingShingle | Chao Yue Tiecheng Xia Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy Advances in Mathematical Physics |
| title | Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy |
| title_full | Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy |
| title_fullStr | Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy |
| title_full_unstemmed | Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy |
| title_short | Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy |
| title_sort | algebro geometric solutions of the coupled chaffee infante reaction diffusion hierarchy |
| url | http://dx.doi.org/10.1155/2021/6618932 |
| work_keys_str_mv | AT chaoyue algebrogeometricsolutionsofthecoupledchaffeeinfantereactiondiffusionhierarchy AT tiechengxia algebrogeometricsolutionsofthecoupledchaffeeinfantereactiondiffusionhierarchy |