![](https://assets.cambridge.org/97805213/69527/cover/9780521369527.gif)
Book contents
- Frontmatter
- Contents
- Preface
- 1 The ionosphere and magnetosphere
- 2 The basic equations
- 3 The constitutive relations
- 4 Magnetoionic theory 1. Polarisation and refractive index
- 5 Magnetoionic theory 2. Rays and group velocity
- 6 Stratified media. The Booker quartic
- 7 Slowly varying medium. The W.K.B. solutions
- 8 The Airy integral function and the Stokes phenomenon
- 9 Integration by steepest descents
- 10 Ray tracing in a loss-free stratified medium
- 11 Reflection and transmission coefficients
- 12 Ray theory results for isotropic ionosphere
- 13 Ray theory results for anisotropic plasmas
- 14 General ray tracing
- 15 Full wave solutions for isotropic ionosphere
- 16 Coupled wave equations
- 17 Coalescence of coupling points
- 18 Full wave methods for anisotropic stratified media
- 19 Applications of full wave methods
- Answers to problems
- Bibliography
- Index of definitions of the more important symbols
- Subject and name index
16 - Coupled wave equations
Published online by Cambridge University Press: 06 December 2010
- Frontmatter
- Contents
- Preface
- 1 The ionosphere and magnetosphere
- 2 The basic equations
- 3 The constitutive relations
- 4 Magnetoionic theory 1. Polarisation and refractive index
- 5 Magnetoionic theory 2. Rays and group velocity
- 6 Stratified media. The Booker quartic
- 7 Slowly varying medium. The W.K.B. solutions
- 8 The Airy integral function and the Stokes phenomenon
- 9 Integration by steepest descents
- 10 Ray tracing in a loss-free stratified medium
- 11 Reflection and transmission coefficients
- 12 Ray theory results for isotropic ionosphere
- 13 Ray theory results for anisotropic plasmas
- 14 General ray tracing
- 15 Full wave solutions for isotropic ionosphere
- 16 Coupled wave equations
- 17 Coalescence of coupling points
- 18 Full wave methods for anisotropic stratified media
- 19 Applications of full wave methods
- Answers to problems
- Bibliography
- Index of definitions of the more important symbols
- Subject and name index
Summary
Introduction
For wave propagation in a stratified medium, the idea of writing the governing differential equations as a set of coupled equations has already been used in §§ 7.8, 7.15, for the study of W.K.B. solutions. The term ‘coupled equations’ is usually given to a set of simultaneous ordinary linear differential equations with the following properties:
(1) There is one independent variable which in this book is the height z or a linear function of it.
(2) The number of equations is the same as the number of dependent variables.
(3) In each equation one dependent variable appears in derivatives up to a higher order than any other. The terms in this variable are called ‘principal’ terms and the remaining terms are called ‘coupling’ terms.
(4) The principal terms contain a different dependent variable in each equation, so that each dependent variable appears in the principal terms of one and only one equation.
It is often possible to choose the dependent variables so that the coupling terms are small over some range of z. Then the equations may be solved by successive approximations. As a first approximation the coupling terms are neglected, and the resulting equations can then be solved. The values thus obtained for the dependent variables are substituted in the coupling terms and the resulting equations are solved to give a better approximation. Some examples of this process are given in § 16.13.
- Type
- Chapter
- Information
- The Propagation of Radio WavesThe Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere, pp. 480 - 519Publisher: Cambridge University PressPrint publication year: 1985