• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.351-367
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• 2011

In this article, we construct exact traveling wave solutions for nonlinear PDEs in mathematical physics via the (1+1)- dimensional combined Korteweg- de Vries and modified Korteweg- de Vries (KdV-mKdV) equation, the (1+1)- dimensional compouned Korteweg- de Vries Burgers (KdVB) equation, the (2+1)- dimensional cubic Klien- Gordon (cKG) equation, the Generalized Zakharov- Kuznetsov- Bonjanmin- Bona Mahony (GZK-BBM) equation and the modified Korteweg- de Vries - Zakharov- Kuznetsov (mKdV-ZK) equation, by using the (($\frac{G'}{G}$) -expansion method combined with the Riccati equation, where G = $G({\xi})$ satisfies the Riccati equation $G'({\xi})=A+BG^2$ and A, B are arbitrary constants.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.173-181
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• 2000

The objective of this paper is to study two dimensional steady gravitational waves on the interface between two immiscible, inviscid and incompressible fluids bounded above by a horizontal rigid boundary and below by a rigid step. A KdV equation for the first order perturbation in an asymptotic expansion can appear. However the coefficient of the KdV theory fails in that case. By a unified asymptotic method, we overcome this difficulty and derive a modified KdV equation with forcing. We find homogeneous steady solutions and present numerical solutions.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.479-490
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• 1997

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio $\rho$ yields a condition $1 + h\rho = (2-h)((1-h)^2 + 4\rho h)^{1/2}$. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV (FKdV) equation fails.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.129-137
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• 1997

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio ρ yields a condition 1＋hρ=(2-h)((1-h)²＋4ρh)/sup 1/2/. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV(FKdV) equaition fails.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.383-395
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• 2010

In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ($\frac{G'}{G}$)- expansion method, where $G\;=\;G(\xi)$ satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

• Journal of Periodontal and Implant Science
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• v.28 no.2
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• pp.281-291
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• 1998

Chitosan is a biodegradable and non-toxic material with a molecular weight of 800-1,500Kd which can be obtained in various forms with extraordinary chemical structures and biological characteristics of which enables it to be used in many fields as a biomaterial. Ion irradiation is a useful tool to modify chemical structures and physical properties of high molecular weight polymers. The basic hypothesis of this study is that when surface properties of chitosan in a sponge form are modified with ion beam-irradiation and cell adhesion properties of chitosan would improve and thereby increase the regenerative ability of the damaged bone. The purpose of this study was to illuminate the changes in the cytocompatibility of chitosan sponges after ion beam-irradiation as a preliminary research. Argon($Ar^+$) ions were irradiated at doses of $5{\times}10^{13}$, $5{\times}10^{15}$ at 35 keV on surfaces of each sponges. Cell adhesion and activity of alkaline phosphatases were studied using rat fetal osteoblasts. The results of this study show hat ion beam-irradiation at optimal doses($5{\times}10^^{13}\;Ar^+\;ion/cm^2$) is a useful method to improve cytocompatibility without sacrificing cell viability and any changing cell phenotypes. These results show that ion beam-irradiated chitosan sponges can be further applied as carriers in tissue engineering and as bone filling materials.

• KSBB Journal
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• v.5 no.3
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• pp.279-291
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• 1990

Partial hydrolysed and deacetylated chitin, CHITA and CHITB as supports of immobilized enzyme were obtained by treatment of acid and base respectively. Glutaraldehyde, bifunctional reagent, was employed for crosslinking between $\beta$-glucosidase and support. Immobilized enzyme activities of CHITA-Gase and CHITB-Gase were determined with the reaction of p-nitrophenol-$\beta$-D-glucopyranoside(PNG) in batch reactor, CSTR and PFR. Their optimum temperature, pH and enzymatic characteristics including Km and Vmax values were observed with variation of the flow rates. Mass transfer coefficient(h), effectiveness factor(η), deactivation rate(kd ) of two immobilized enzymes were also examined to compare efficiency of reactors.