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Existence of non-topological multi-string solutions for a gravitational $ O(3)$ gauge field model


Authors: Nari Choi and Jongmin Han
Journal: Proc. Amer. Math. Soc. 147 (2019), 1429-1445
MSC (2010): Primary 35J61, 35Q75, 81T13
DOI: https://doi.org/10.1090/proc/14182
Published electronically: December 31, 2018
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Abstract: In 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.


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Additional Information

Nari Choi
Affiliation: Department of Statistics, Ewha Womans University, Seoul, 03760, Korea
Email: nrchoi@khu.ac.kr

Jongmin Han
Affiliation: Department of Mathematics, Kyung Hee University, Seoul, 02447, Korea
Email: jmhan@khu.ac.kr

DOI: https://doi.org/10.1090/proc/14182
Received by editor(s): October 23, 2017
Received by editor(s) in revised form: April 3, 2018
Published electronically: December 31, 2018
Additional Notes: The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2015R1D1A1A01057499).
Communicated by: Joachim Krieger
Article copyright: © Copyright 2018 American Mathematical Society