• 대한수학회지
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• 제32권3호
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• 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.

• 충청수학회지
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• 제24권2호
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• pp.359-370
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• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.

• Bulletin of the Korean Chemical Society
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• 제35권9호
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• pp.2699-2703
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• 2014

We solve the Klein-Gordon equation with the modified Rosen-Morse potential energy model. The bound state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $6^1{\Pi}_u$ state of the $^7Li_2$ molecule have been computed by using the modified Rosen-Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

• 정보처리학회논문지A
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• 제11A권7호
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• pp.571-576
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• 2004

비선형 클라인 고든 방정식의 수치해를 구하기 위해 라그란제 보간을 사용하는데 비선형 항을 계산하기위해 보간식의 차이가 거의 없는 변형된 식을 사용하여 해의 .안정성과 해의 수렴성을 밝히고 오차를 분석하였다. 즉 $I(x)^{3}$ 대신에 $f(x_i)^{3}I_i(x)$을 사용하였으며 오차는 $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ 이하임을 보였고 석기서 N은 다항식의 차수이다.

• 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.