• 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.

• 대한수학회보
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• 제60권6호
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• pp.1697-1704
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• 2023

We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

• 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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• 제46권5호
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• pp.1105-1117
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• 2009

In this paper a parameter identification problem for a damped sine-Gordon equation is studied from the theoretical and numerical perspectives. A spectral method is developed for the solution of the state and the adjoint equations. The Powell's minimization method is used for the numerical parameter identification. The necessary conditions for the optimization problem are shown to yield the bang-bang control law. Numerical results are discussed and the applicability of the necessary conditions is examined.

• 한국컴퓨터산업학회논문지
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• 제3권5호
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• pp.569-574
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• 2002

유계된 정의역에서 sine-Gordon 방정식인 현수교의 과격한 운동의 모델을 만든다. 유한 차분법을 이용하여 비선형 미분방정식을 수치 해석학적으로 풀다. 이 미분방정식은 다중 주기근을 가지고 있다. 다리가 큰 진폭이나 작은 진폭으로 진동하는 것은 초기의 변위와 속도에만 달려있다. 게다가, 많은 현상들이 Tacoma Narrows가 붕괴된 날에 관찰되는 것과 일치하고 있다.