scholarly journals An exact vectorial spectral representation of the wave equation for propagation over a Terrain in 3D

2013 ◽  
Author(s):  
A. Chabory ◽  
C. Morlaas ◽  
R. Douvenot
Keyword(s):  
Wave Equation ◽  
Spectral Representation

Spectral representation and scattering theory for the wave equation with two unbounded media

1993 ◽  
Vol 113 (2) ◽  
pp. 423-447 ◽  
Author(s):  
G. F. Roach ◽  
Bo Zhang
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Stationary Phase ◽  
Scattering Theory ◽  
Spectral Representation ◽  
Fourier Transforms ◽  
Eigenfunction Expansions ◽  
Wave Operators ◽  
Unbounded Media ◽  
Generalized Eigenfunction

AbstractIn this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

DeWitt geometry and the wave equation in hyper-volume

2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Equation

DeWitt geometry and the wave equation in hyper-volume

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