| Autor: |
E.O. Ifidon, E.O. Oghre |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Journal of the Nigerian Mathematical Society. 34(2):216-226 |
| ISSN: |
0189-8965 |
| DOI: |
10.1016/j.jnnms.2014.12.002 |
| Popis: |
A nonlinear elliptic partial differential equation (pde) is obtained as a generalization of the planar Euler equation to the surface of the sphere. A general solution of the pde is found and specific choices corresponding to Stuart vortices are shown to be determined by two parameters λ and N which characterizes the solution. For λ = 1 and N = 0 or N = − 1 , the solution is globally valid everywhere on the sphere but corresponds to stream functions that are simply constants. The solution is however non-trivial for all integral values of N ≥ 1 and N ≤ − 2 . In this case, the solution is valid everywhere on the sphere except at the north and south poles where it exhibits point-vortex singularities with equal circulation. The condition for the solutions to satisfy the Gauss constraint is shown to be independent of the value of the parameter N . Finally, we apply the general methods of Wahlquist and Estabrook to this equation for the determination of (pseudo) potentials. A realization of this algebra would allow the determination of Backlund transformations to evolve more general vortex solutions than those presented in this paper. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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