Chern-Simons gauged sigma model into $ \mathbb{H}^2 $ and its self-dual equations

Kwangseok Choe; Hyungjin Huh

doi:10.3934/dcds.2019189

Article Contents

2019, Volume 39, Issue 8: 4613-4646. Doi: 10.3934/dcds.2019189

This issue Previous Article On fractional nonlinear Schrödinger equation with combined power-type nonlinearities Next Article Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces

Chern-Simons gauged sigma model into $ \mathbb{H}^2 $ and its self-dual equations

Kwangseok Choe^1, and
Hyungjin Huh^2, ,

1.
Department of Mathematics, Inha University, Incheon, 22212, Republic of Korea
2.
Department of Mathematics, Chung-Ang University, Seoul, 06974, Republic of Korea

^*Corresponding author: Hyungjin Huh
^*Corresponding author: Hyungjin Huh

Received: August 31, 2018

Revised: January 31, 2019

Published: May 2019

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Abstract

We propose the Chern-Simons gauged sigma model from $\mathbb{R}^{1+2}$ into the hyperbolic plane $\mathbb{H}^2$. We seek a static configuration of this model and derive self-dual equations. We also establish some existence results for solutions of the self-dual equations under appropriate boundary conditions near $\infty$

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Mathematics Subject Classification: Primary: 81T13; Secondary: 35B40.

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