• Title/Summary/Keyword: Wave equation

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REMARKS ON THE INFINITY WAVE EQUATION

  • Huh, Hyungjin
    • 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.

THE UNIQUE EXISTENCE OF WEAK SOLUTION TO THE CURL-BASED VECTOR WAVE EQUATION WITH FIRST ORDER ABSORBING BOUNDARY CONDITION

  • HYESUN NA;YOONA JO;EUNJUNG LEE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.27 no.1
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    • pp.23-36
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    • 2023
  • The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

Prediction of Wave Transformation in the Kwangan Beach (광안해역에서의 파랑변형예측)

  • 박정철;김재중;김인철
    • Journal of Ocean Engineering and Technology
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    • v.15 no.2
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    • pp.6-10
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    • 2001
  • 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 develope as wave-current equation type to investigate the effect of wave-current interaction. It starts from Berkhoff's(1972) mild slope equation and is transformed to time-dependent hyperbolic type equation by using variational principal. Finally the governing equation is shown as a parabolic type equation by splitting method. 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.

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KINK WAVE SOLUTIONS TO KDV-BURGERS EQUATION WITH FORCING TERM

  • Chukkol, Yusuf Buba;Muminov, Mukhiddin
    • 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.

Numerical method of hyperbolic heat conduction equation with wave nature (파동특성을 갖는 쌍곡선형 열전도방정식에 관한 수치해법)

  • 조창주
    • Journal of Advanced Marine Engineering and Technology
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    • v.22 no.5
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    • pp.670-679
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    • 1998
  • The solution of hyperbolic equation with wave nature has sharp discontinuties in the medium at the wave front. Difficulties encounted in the numrtical solution of such problem in clude among oth-ers numerical oscillation and the representation of sharp discontinuities with good resolution at the wave front. In this work inviscid Burgers equation and modified heat conduction equation is intro-duced as hyperboic equation. These equations are caculated by numerical methods(explicit method MacCormack method Total Variation Diminishing(TVD) method) along various Courant numbers and numerical solutions are compared with the exact analytic solution. For inviscid Burgers equa-tion TVD method remains stable and produces high resolution at sharp wave front but for modified heat Conduction equation MacCormack method is recommmanded as numerical technique.

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APPLICATION OF ROTHE'S METHOD TO A NONLINEAR WAVE EQUATION ON GRAPHS

  • Lin, Yong;Xie, Yuanyuan
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.745-756
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    • 2022
  • We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |ut|p-1·ut (p > 1).

TRAVELING WAVE SOLUTIONS TO THE HYPERELASTIC ROD EQUATION

  • MOON, BYUNGSOO
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.261-273
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    • 2015
  • We consider the hyperelastic rod equation describing nonlinear dispersive waves in compressible hyperelastic rods. We investigate the existence of certain traveling wave solutions to this equation. We also determine whether two other equations(the b-family equation and the modified Camassa-Holm equation) have our solution type.

A Study on the Determination of Wave Load Acting on Offshore Structures (해저 석유개발을 위한 해양구조물의 기본 설계/해석 및 실험기법 개발 -해양구조물에 작용하는 파랑하중 산정에 관한 연구)

  • 이근무
    • Journal of Ocean Engineering and Technology
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    • v.14 no.1
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    • pp.6-10
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    • 2000
  • In this paper various methods of determining of wave loads acting ofshore structures including impact load due to breaking wave are studied and corresponding model test was performed. In the theoretical approach wave load by nonbreaking wave and impact load by breaking wave is determined by Morrison's equation Goda's equation and impact wave equation, In the experimental approach wave load by nonbreaking wave acting on cylindrical pile used in offshore structures is determined by measuring the strain on a cylindrical pile and compared with theoretical calue. in the numerical approach impact load by breaking wave acting on a modeled cylindrical pile is calculated by usign ANSYS FEM program and compared with theoretical value. It is found that the experimental and numerical results are comparable to theoretical results, Thus the determination of wave load acting on offshore structures can be obtained by a proposed methods and it acceptable.

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TRAVELING WAVE SOLUTIONS FOR HIGHER DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS USING THE $(\frac{G'}{G})$- EXPANSION METHOD

  • Zayed, E.M.E.
    • 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.

The Characteristics of Pulsating Flow in a Hydraulic Pipe (유압관로에서 맥동유동 특성에 관한 연구)

  • 모양우;유영태;김지화
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.13 no.7
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    • pp.653-665
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    • 2001
  • The characteristics of the pulsating flow in a hydraulic pipe have been investigated. It is necessary to study the power control of the power transmission system in the landing gear system of aircraft and the design of robots. In this system, the power transmission pipeline is composed of a hydraulic system, and the operating flow is unsteady flow. The wave equation varying with frequency is analyzed in order to investigate the characteristics of unsteady flow in such a pipe. This wave equation involves the propagation coefficient in terns of frequency and viscosity. The theoretical result of this wave equation are compared with experimental result. Each wave equation, varying with the propagation coefficient, is analyzed theoretically. then, a sinusoidal wave generator is built in order to make better sinusoidal waves, and a rectifier is built to eliminate the noise from the hydraulic pump. The theoretical results of the wave equation in the flow of viscous fluid agree well with experimental results.

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