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Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data
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"... We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of BartolucciChenLinTarantello it is proved that the profile of the solutions dif ..."
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We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of BartolucciChenLinTarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
ELECTRICALLY AND MAGNETICALLY CHARGED VORTICES IN THE CHERN–SIMONS–HIGGS THEORY
"... ABSTRACT. In this paper, we prove the existence of finiteenergy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory for which both the Maxwell term and Chern–Simons term are present in the Lagrangian density. We consider both Abelian and nonAbelian cases. T ..."
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ABSTRACT. In this paper, we prove the existence of finiteenergy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory for which both the Maxwell term and Chern–Simons term are present in the Lagrangian density. We consider both Abelian and nonAbelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a longstanding open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern–Simons term. 1.
On the BornInfeld Abelian Higgs cosmic strings with symmetric vacuum
"... We study a system of elliptic equations from the Abelian BornInfeld system coupled with the Einstein equations under the boundary condition of the symmetric vacuum(nontopological type). When the total string number satisfies 1 ≤ N < 1 4πG, where G is the gravitational constant, we construct a famil ..."
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We study a system of elliptic equations from the Abelian BornInfeld system coupled with the Einstein equations under the boundary condition of the symmetric vacuum(nontopological type). When the total string number satisfies 1 ≤ N < 1 4πG, where G is the gravitational constant, we construct a family of solutions to the system. The qualitative properties of the solutions are quite different from the solutions with the boundary condition of the broken vacuum symmetry.
Existence of the Semilocal ChernSimons
"... We consider the Bogomol’nyi equations of the Abelian ChernSimonsHiggs model with SU(N)global ⊗ U(1)local symmetry. This is a generalization of the wellknown Abelian ChernSimonsHiggs model with U(1)local symmetry. We prove existence of both topological and nontopological multivortex solutions of ..."
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We consider the Bogomol’nyi equations of the Abelian ChernSimonsHiggs model with SU(N)global ⊗ U(1)local symmetry. This is a generalization of the wellknown Abelian ChernSimonsHiggs model with U(1)local symmetry. We prove existence of both topological and nontopological multivortex solutions of the system on the plane. 1