Nari Choi
Hanyang University · 物理学・天文学
研究室紹介
Professor Nari Choi's research lab specializes in nonlinear partial differential equations arising from theoretical physics, particularly in the context of gauge field theories and gravity. The lab focuses on the existence, asymptotic behavior, and geometric properties of solutions to self-dual equations in Chern-Simons and Maxwell–Ginzburg–Landau type models coupled with gravity. Key research directions include nontopological and multi-string solutions, vortex solutions, and their topological and curvature invariants. The group employs advanced analytical techniques such as the implicit function theorem, degree theory, and perturbation methods.
Research Overview
Research Output Trend
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Selected Papers
5In this paper, we consider the self-dual equation arising from the Maxwell gauged $O(3)$ model coupled with gravity. We prove the existence of non-topological multi-string solutions and obtain their decay estimates at infinity. Using the decay rates, we compute the static energy, the magnetic flux, and the total Gaussian curvature corresponding to our solutions. Our solutions are constructed by a perturbation argument with an application of the Implicit Function Theorem.
In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter <TEX>${\tau}{\in}[-1,1</TEX><TEX>]</TEX><TEX>$</TEX> appearing in the nonlinear term. The case <TEX>${\tau}=1$</TEX> lies on the borderline for the existence of solutions in the previous results [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if
We consider an elliptic equation induced from the Maxwell gauged O(3) sigma model coupled with gravity. In particular, we study the main equation as two cases: one is for only string and the other is for anti-string. On the compact surface, we prove the existence of ɛ-dependent solutions for each case by using the super-sub solutions method. Moreover, we find the second solution by using the Leray–Schauder degree theory. Furthermore, we estimate the asymptotic behavior of our solution as ɛ → 0.