AI 中文总结
本文证明金兹堡-朗道方程的标准二度、三度涡旋解非退化并计算其莫尔斯指数，所用方法可推广至更高阶解的研究。
AI 中文摘要
我们证明金兹堡-朗道方程的标准二度和三度涡旋解是非退化的，同时计算了它们的莫尔斯指数。该证明依赖于这些解模的新显式上下界及比较论证，预计该方法可推广用于研究更高阶解。
英文摘要
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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