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Stuart Vortices Extended to a Sphere Admits Infinite-Dimensional Generalized Symmetries

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To generalize Stuart vortices to the surface of a sphere, Crowdy recently obtained a nonlinear partial differential equation (involving a parameter ) that has no known solution except for = 0 for which he gives a solution [ 1]. = 0 is therefore, assumed to be a kind of “solvability” condition for the equation. In this paper, to examine the integrability of this equation, we apply a generalized form of the Wahlquist–Estabrook prolongation procedure given in [ 2] to the equation for all nonzero values of  . We see that the generalized symmetries of the Stuart vortices when extended to the surface of a sphere are infinite dimensional for all nonzero values of  and are isomorphic to which becomes the minimal prolongation algebra of the equation.
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Document Type: Research Article

Affiliations: University of Benin, Nigeria

Publication date: October 1, 2010

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