• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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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.

• Honam Mathematical Journal
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• v.30 no.4
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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.

• The KIPS Transactions:PartA
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• v.11A no.7 s.91
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• pp.571-576
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• 2004

In this paper, by using Lagrange polynomial interpolation with a trick such that for $f(x)^{3}$ we shall use $f(x_i)^{3}I_i(x)^{3}$ instead of $I(x)^{3}$ where $I{x}{\;}={\;}\sum_{i}^{f}(x_i)I_i(x)$. We show the convergence and stability and calculate errors. These errors are approximately less than $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ where N is a polynomial degree.