| Autor: |
Jiawei Hu, Ning Zhang |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Symmetry, Vol 16, Iss 10, p 1258 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2073-8994 |
| DOI: |
10.3390/sym16101258 |
| Popis: |
The Fokas method exhibits remarkable versatility in solving boundary value problems associated with both linear and nonlinear partial differential equations, particularly when conventional approaches encounter challenges in handling intricate boundary conditions. The existing literature often lacks the incorporation of unconventional boundary conditions, and this study addresses this issue by extending the application of the Fokas method to the higher-order Gerdjikov-Ivanov equation on the half line (−∞,0]. We have demonstrated the exclusive representation of the potential function u(z,t) in the higher-order Gerdjikov–Ivanov equation through the solution of a Riemann–Hilbert problem. The characteristic function is partitioned on the complex plane, and we obtain the jump matrix between each partition based on the positive and negative values of the partition as well as the spectral matrix determined by the initial data and boundary value data. The findings suggest that the spectral functions are not mutually independent; instead, they conform to a global relationship. The novel aspect of this study is the application of the Fokas method to a previously unexplored case, contributing to the theoretical and practical understanding of complex partial differential equations and filling a gap in the treatment of boundary conditions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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