• 대한수학회지
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• 제58권5호
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• pp.1131-1145
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• 2021

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

• 대한수학회보
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• 제56권6호
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• pp.1447-1465
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• 2019

In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_0$, we prove the existence and uniqueness of the mild solution via the iteration method.

• 대한수학회보
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• 제55권2호
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• pp.591-598
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• 2018

This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.39-78
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• 2020

In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

• 새물리
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• 제68권11호
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• pp.1225-1230
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• 2018

Schwinger pair production of electrons and positrons in a strong electric field is a prediction of nonperturbative quantum field theory, in which the out-vacuum is superposed of multi-particle states of the in-vacuum. Solving the Dirac or Klein-Gordon equation in the background field, though a linear wave equation, and finding the pair-production rate is a difficult or nontrivial job. The phase-integral method has recently been introduced to compute the pair production in space-dependent electric fields, and a complex analysis method has been employed to calculate the pair production in time-dependent electric fields. In this paper, we apply the complex analysis method to a Sauter-type electric field and other hyperbolic-type electric fields that vanish in the past and future and show that the Stokes phenomena in pair production occur when the time-dependent frequency for a given momentum has finite simple poles (polons) with pure imaginary residues.