The existence of topological solutions to the Chern-Simons model on lattice graphs

2023/10/21 by Hua, Bobo, Huang, Genggeng, Wang, Jiaxuan · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2310.13905

Abstract

We prove the existence of topological solutions to the self-dual Chern-Simons model and the Abelian Higgs system on the lattice graphs Zⁿ for n>1. This extends the results in Huang, Lin and Yau [HLY20] from finite graphs to lattice graphs.

Cited by

• Topological solutions of generalized Chern-Simons equations on discrete lattice graphs
• Existence, asymptotic behaviors, and high-dimensional uniqueness of topological solutions to the skew-symmetric Chern-Simons system on lattice graphs
• On finite-energy solutions of Kazan-Warner equations on the lattice graph
• Existence theory for elliptic equations of general exponential nonlinearity on finite graphs

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