TY - JOUR

T1 - VORTEX CONDENSATION IN GENERAL U(1)×U(1) ABELIAN CHERN-SIMONS MODEL ON A FLAT TORUS

AU - Huang, Hsin Yuan

N1 - Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/8

Y1 - 2022/8

N2 - In this paper, we study an elliptic system arising from the U(1)×U(1) Abelian Chern-Simons Model[25, 37] of the form (Formula presented) (1) which are defined on a parallelogram Ω in R2 with doubly periodic boundary conditions. Here, a and b are interaction constants, λ > 0 is related to coupling constant, mj > 0(j = 1, · · ·, k1), nj > 0(j = 1, · · ·, k2), δp is the Dirac measure, p is called vortex point. Concerning the existence results of this system over Ω, only the cases (a, b) = (0, 1)[28] and a > b > 0[14] were studied in the literature. The solvability of this system (1) is still an open problem as regards other parameters (a, b). We show that the system (1) admits topological solutions provided λ is large and b > a > 0 Our arguments are based on a iteration scheme and variational formulation.

AB - In this paper, we study an elliptic system arising from the U(1)×U(1) Abelian Chern-Simons Model[25, 37] of the form (Formula presented) (1) which are defined on a parallelogram Ω in R2 with doubly periodic boundary conditions. Here, a and b are interaction constants, λ > 0 is related to coupling constant, mj > 0(j = 1, · · ·, k1), nj > 0(j = 1, · · ·, k2), δp is the Dirac measure, p is called vortex point. Concerning the existence results of this system over Ω, only the cases (a, b) = (0, 1)[28] and a > b > 0[14] were studied in the literature. The solvability of this system (1) is still an open problem as regards other parameters (a, b). We show that the system (1) admits topological solutions provided λ is large and b > a > 0 Our arguments are based on a iteration scheme and variational formulation.

KW - Chern-Simons model

KW - super-sub solution method

KW - topological solutions

KW - variational method

UR - http://www.scopus.com/inward/record.url?scp=85134607945&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2021234

DO - 10.3934/dcdsb.2021234

M3 - Article

AN - SCOPUS:85134607945

SN - 1531-3492

VL - 27

SP - 4415

EP - 4428

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 8

ER -