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arXiv · 2608.04976

Nondegeneracy and Morse Index of Ginzburg--Landau Vortices

Manuel del Pino·Yong Liu·Monica Musso·Juncheng Wei·Wen Yang
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Abstract

We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies on new explicit upper and lower bounds of the modulus of these solutions and a comparison argument. It is expected that our method can be generalized to study higher degree solutions.

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Manuel del Pino, Yong Liu, Monica Musso, Juncheng Wei, Wen Yang. 2026-08-05. Nondegeneracy and Morse Index of Ginzburg--Landau Vortices. https://arxiv.org/abs/2608.04976

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