• Honam Mathematical Journal
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• v.33 no.2
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• pp.247-259
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• 2011

In this paper, the $(\frac{G'}{G})$-expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.191-192
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• 2003

A numerical method for a wave diffraction problem in three-dimensional channels is developed. The physical models are various shapes of channel connected to the open sea. When a ship or an offshore structure is moored in various configurations of channel connected to an open sea, the prediction of the hydrodynamic force exerting on the moored ship could be important for the prediction of its motion. It is assumed that the fluid is inviscid and incompressible and its motion is irrotational. From the continuity equation, the Laplace equation can be obtained as the governing equation. The surface tension at free surface is neglected, and wave amplitude is assumed to be small compared to the wave length. Then the free surface condition can be linearized. The numerical method used here is the localized finite element method based on a variational formulation

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.611-624
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• 2010

A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.16 no.4
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• pp.233-240
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• 2004

For the development of empirical equation of run-up height, a new surf parameter called' wave action slope' $S_x$ is introduced. Approximate equation has been produced for each band of water depth for the computation of wave run-up height using the laboratory graph of Saville(1958). On the other hand using the laboratory data of Ahrens(1988) and Mase(1989), empirical equations of run-up height have been developed for the general application with considering roughness effect covering a wide range of water depth and wall slope. When Mase tried to relate the run-up height to the Iribarren number, nonlinear relation has been obtained and hence the empirical equation has a power law. But when the wave action slope is adopted as a major factor for the estimation of run-up height the empirical equation shows a linear relationship with very good correlation for the wide range of water depth and wall slope.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.4 no.4
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• pp.236-241
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• 2011

Mechanical properties of cancellous bone with a high porosity and cortical bone with a high fraction of solid are estimated by the measurement of ultrasonic wave propagation. The speed of sound (SOS) in ultrasonic waves is usually measured by two equations, bulk wave equation and bar wave equation. Bulk wave speed has almost same as the fast wave of Biot's theory. In this study, we examine whether the bulk wave speed is influenced by the anisotropy of bone matrix. The SOS when the bone matrix is isotropy is 0.69% faster than that when the bone matrix is transversely isotropy. We also examine if the use of bar equation is adequate for a cortical bone. In the previous paper, the bar wave speed is a function of Young's modulus or elastic coefficient tensor. In the same manner, the effect of bar wave speed to isotropic and anisotropic bone is estimated.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.81-93
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• 2009

Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.

• Earthquakes and Structures
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• v.9 no.2
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• pp.305-320
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• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.2
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• pp.55-61
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• 1987

The wave system due to a moving submerged body is investigated both theoretically and numerically. Boussinesq equation, which is derived under the assumption that the effects of nonlinearity and wave dispersion are of the same order, is generalized to take the forcing agency into account. Furthermore, under the more restrive assumption that the disturbance is of higher order, inhomogeneous Korteweg-de Vries equation is derived. These equations are solved numerically to obtain the generated wave system and the wave-making resistance. These results are compared with those given by the linear theory.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.04a
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• pp.75-81
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• 2000

Water waves propagate over irregular bottom bathymetry are transformed by refraction, diffraction, shoaling, reflection etc. Principal factor of wave transform is bottom bathymetry, but in case of current field, current is another important factor which effect wave transformation. The governing equation of this study is develop as wave-current equation type to investigate the effect of wave-current interaction. This wave-current model was applied to the Kwangan beach which is located at Pusan. The numerical simulation results of this model show the characteristics of wave transformation and flow pattern around the Kwangan beach fairly well.