• 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.

• 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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• 제28권5_6호
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• pp.1227-1237
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• 2010

In this paper, a Klein-Gordon equation is solved by using the homotopy analysis method (HAM), homotopy perturbation method (HPM) and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. The uniqueness of the solution and the convergence of the proposed methods are proved. The accuracy of these methods are compared by solving an example.

• Bulletin of the Korean Chemical Society
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• 제31권12호
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• pp.3573-3578
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• 2010

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

• 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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• 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].

• 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.

• 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.

• 한국가정과교육학회지
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• 제12권3호
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• pp.1-17
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• 2000

The purpose of this research was to apply and conduct a class with Gordon’s Creative Problem Solving Method(Synectics) to the area of ’human development and family relations’among male students in a jr. high school. Subject matters which were appropriate for applying Gordon’s Creative Problem Solving method were selected from ’human development and family relations’area, with problem circumstances set to reflect to the highest degree the interests of individuals and families. An 8 hour teaching instructional guide was constructed with $\boxdr$strategy 1$\boxul$of Gordon’s Creative Problem Solving method in order to solve creatively the established problem. This was practically implied to 70 students(each class had 34 and 36 students respectively) in K middle school located in Seoul. The period of this application was for 3 months during March through May of 1999. The perception of this method was examined by the teachers and students through open-ended questions. The record of perception showed that 56 students out of 70(with no response from 5 students) through that the class done by the creativity problem solving method was good. The majority of reasons mentioned for the positive answers were ’being able to receive different thoughts which were unusual of daily life’. In addition the students who participated in the class were able to foster a joint experience which improved their understanding of relationships and sens of community. moreover students who did not do well n the class or were diffident were encouraged to participate which in result showed that there was even an internal effect.

• 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.