arXiv subjects

Ardian N. Atmaja

Publications and source records attributed to Ardian N. Atmaja.

3 recordsLinked to original sources

arXiv2025

The Global Existence and Uniqueness of Maxwell-Chern-Simons-Higgs Equation in (2+1) Dimensions

In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system coupled to a neutral scalar with nontrivial scalar potential on (2+1) dimensional Minkowski spacetime. Our methods rely only on classical existence theorems, including energy estimates, the Sobolev inequality, and the choice of the Coulomb gauge condition. The equations are well-posed for finite initial data and the solution preserves any additional $H^{s}$ regularity for $s>0$ in the data.

math.AP↗

arXiv2024

Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordström Spacetimes

In this paper, we prove the uniform energy bound for the Maxwell-Higgs system in the exterior region of Reissner-Nordström black holes. By employing an integrated local energy decay (ILED) estimate in combination with the Sobolev embedding theorem on a compact Riemannian manifold, we derived $L^\infty$ bounds for the fields. These results were then used to obtain a bound for the conformal energy of the system using the Cauchy-Schwarz inequality and Hardy-type inequalities.

math.AP↗

arXiv2014

On Bogomol'nyi Equations of Classical Solutions

We review the Bogomol'nyi equations and investigate an alternative route in obtaining it. It can be shown that the known BPS equations can be derived directly from the corresponding Euler-Lagrange equations via separation of variables, without having to appeal to the Hamiltonian. We apply this technique to the Dirac-Born-Infeld solitons and obtained the corresponding equations and the potentials. This method is suitable for obtaining the first-order equations and determining the allowed potentials for noncanonical defects.

hep-th↗