• 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.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Journal of Korean Association for Spatial Structures
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• v.17 no.3
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• pp.75-82
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• 2017

The Kingery-Bulmash equation is the most common equation to calculate blast load. However, the Kingery-Bulmash equation is complicated. In this paper, a modified equation for surface blast load is proposed. The equation is based on Kingery-Bulmash equation. The proposed equation requires a brief calculation process, and the number of coefficients is reduced under 5. As a result, each parameter obtained by using the modified equation has less than 1% of error range comparing with the result by using Kingery-Bulmash equation. The modified equation may replace the original equation with brief process to calculate.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.389-399
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• 2002

In this paper we solve a quadratic Jensen type functional equation (equation omitted) and prove the stability of this equation.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.451-459
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• 2021

We propose the infinity wave equation which can be derived from the exponential wave equation through the limit p → ∞. The solution of infinity Laplacian equation can be considered as a static solution of the infinity wave equation. We present basic observations and find some special solutions.

• Journal of the Korean Applied Science and Technology
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• v.23 no.3
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• pp.185-191
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• 2006

It is desirable to have an accurate expression on the temperature dependence of surface(or interfacial) tension ${\sigma}$, because most of the interfacial thermodynamic functions can be derived from it. There have been proposed several equations on the temperature dependence of the surface tension, ${\sigma}(T)$. Among them $E{\ddot{o}}tv{\ddot{o}}s$ equation and the one modified by Katayama, which is called Katayama equation, for improving accuracies of $E{\ddot{o}}tv{\ddot{o}}s$ equation close to critical points, have been most well-known. In this article Katayama equation is interpreted on the basis of the cell model to understand the nature of the equation. The cell model results in an expression very similar to Katayama equation. This implies that, although $E{\ddot{o}}tv{\ddot{o}}s$ and Katayama equations were obtained on the basis of experimental results, they have a sound theoretical background. The Katayama equation is also modified with the phase volume replaced with a critical scaling expression. The modified Katayama equation becomes a power-law equation with the exponent slightly different from the value obtained by critical-scaling theory. This implies that Katayama equation can be replaced by a critical-scaling equation which is proven to be accurate.

• 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.

• Bulletin of the Korean Chemical Society
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• v.34 no.12
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• pp.3709-3714
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• 2013

Based on the Debye-H$\ddot{u}$ckel equation, a semi-empirical equation for activity coefficients was derived through empirical and theoretical trial and error efforts. The obtained equation included two parameters: the proportional factor and the effective radius of an ionic sphere. These parameters were used in the empirical and regression parameter fitting of the calculated values to the experimental results. The activity coefficients calculated from the equation agreed with the data. Transforming to a semi-empirical form, the equation was expressed with one parameter, the ion radius. The ion radius, ${\alpha}$, was divided into three parameters, ${\alpha}_{cation}$, ${\alpha}_{anion}$ and ${\delta}_{cation}$, representing parameters for the cation, anion and combination, respectively. The advantage of this equation is the ability to propose a semi-empirical equation that can easily determine the activity coefficient with just one parameter, so the equation is expected to be used more widely in actual industry applications.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.117-123
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• 2003

For an n ${\times}$ n real matrix X, let ${\Phi}$(X) = X o (X$\^$-1/)$\^$T/, where o stands for the Hadamard (entrywise) product. Suppose A, B, G and D are n ${\times}$ n real nonsingular matrices, and among them there are at least one solutions to the equation (equation omitted). An equivalent condition which enable (equation omitted) become a real solution ot the equation (equation omitted), is given. As application, we get new real solutions to the matrix equation (equation omitted) by applying the results of Zhang. Yang and Cao [SIAM.J.Matrix Anal.Appl, 21(1999), pp: 642-645] and Chen [SIAM.J.Matrix Anal.Appl, 22(2001), pp:965-970]. At the same time, all solutions of the matrix equation (equation omitted) are also given.