• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.925-934
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• 2012

In this work the sine-Gordon equation will be examined for multiple soliton solutions. The higher dimensional sine-Gordon equations will be studied for multiple soliton solutions as well. The simplified form of the Hirota's method will be employed to conduct this analytic study.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• 대한수학회보
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• 제55권3호
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• pp.699-715
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• 2018

In this paper, we show a proof of Gordon's Conjecture by using Qiu's labels and two new labels.

• 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.

• 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.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2017년도 추계학술대회
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• pp.349-352
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• 2017

2000년대 초반부터 많은 정보보호 관련자들은 정보보호 투자 대비 효과를 측정하고자 노력하였다. 그러한 노력으로 ROSI(Return On Security Investment)를 산출하는 여러 가지 방법 및 ROSI의 Return인 사이버 피해액을 계산하는 Gordon & Loeb 방법 등이 고안되었다. 하지만, 효과를 직접적으로 산출하기 힘든 정보보호의 구조적 특성, 관련 정보의 부족 및 사이버 피해액 산정 시 정성적인 요소가 포함되어 정확한 산출이 어렵다는 문제점이 존재한다. 본 연구는 현재까지의 연구 결과를 살펴보고 기존 방법들 중 가장 효율적이라고 생각되는 Gordon & Loeb 방법과 신진 방법 2가지에 대해 분석하고 개선된 방법을 설계하고자 한다.

• 대한수학회지
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• 제43권5호
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• pp.931-950
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• 2006

We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].

• 대한수학회지
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• 제39권4호
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• pp.509-524
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• 2002

We Study the Problems Of identification for the damped sine-Gordon equations with constant parameters. That is, we establish the existence and necessary conditions for the optimal constant parameters based on the fundamental optimal control theory and the transposition method studied in Lions and Magenes [5].

• 대한수학회보
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• 제57권2호
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• pp.281-294
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• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

• 호남수학학술지
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• 제30권4호
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• pp.631-635
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• 2008

In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.