Wave equation solution by a coupled‐mode, multiple‐reflection series method.

1991 ◽  
Vol 90 (4) ◽  
pp. 2350-2350
Author(s):  
D. M. Pai
Keyword(s):  
Wave Equation ◽  
Multiple Reflection ◽  
Series Method ◽  
Equation Solution ◽  
Coupled Mode

TWO-WAY COUPLED-MODE SOLUTIONS IN THE COMPLEX HORIZONTAL WAVENUMBER PLANE

2008 ◽  
Vol 16 (02) ◽  
pp. 225-256 ◽  
Author(s):  
STEVEN A. STOTTS
Keyword(s):  
Normal Modes ◽  
Lanczos Method ◽  
Numerical Implementation ◽  
Coupling Coefficients ◽  
Equation Solution ◽  
The Real ◽  
Coupled Equations ◽  
Coupled Mode ◽  
Layer Mode ◽  
Mode Solution

A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am.111 (2002) 1623–1643], referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am.96 (1994) 1741–1747]. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

Approximate symmetry analysis of nonlinear Rayleigh-wave equation

2018 ◽  
Vol 15 (04) ◽  
pp. 1850055
Author(s):  
Saeede Rashidi ◽  
S. Reza Hejazi ◽  
Elham Dastranj
Keyword(s):  
Wave Equation ◽  
Power Series ◽  
Small Parameter ◽  
Conservation Laws ◽  
Rayleigh Wave ◽  
Symmetry Analysis ◽  
Approximate Symmetry ◽  
Series Method ◽  
Power Series Method ◽  
New Exact Solutions

In this paper, the Lie approximate symmetry analysis is applied to investigate the new exact solutions of the Rayleigh-wave equation. The power series method is employed to solve some of the obtained reduced ordinary differential equations with a small parameter. We yield the new analytical solutions with small parameter which is effectively obtained by the proposed method. The concept of nonlinear self-adjointness is used to construct the conservation laws for Rayleigh-wave equation. It is shown that this equation is approximately nonlinearly self-adjoint and therefore desired conservation laws can be found using appropriate formal Lagrangians.

Analysis of the validity of the asymptotic techniques in the lower hybrid wave equation solution for reactor applications

2007 ◽  
Vol 14 (11) ◽  
pp. 112506 ◽  
Author(s):  
A. Cardinali ◽  
L. Morini ◽  
C. Castaldo ◽  
R. Cesario ◽  
F. Zonca
Keyword(s):  
Wave Equation ◽  
Lower Hybrid ◽  
Hybrid Wave ◽  
Lower Hybrid Wave ◽  
Equation Solution

An improved approach for the wave equation solution of graded‐index waveguide

1995 ◽  
Vol 78 (5) ◽  
pp. 3514-3516
Author(s):  
In Kim ◽  
Byung‐Doo Choe ◽  
Weon Guk Jeong
Keyword(s):  
Wave Equation ◽  
Equation Solution ◽  
Graded Index
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