Book contents
- Frontmatter
- Contents
- Preface to the Second Edition
- Preface to the First Edition, 2000
- Acknowledgments
- PART I Basic Phenomenology
- PART II Physical Models
- 6 Self-Gravity and Relation to Plasma Physics
- 7 Relaxation Times, Absence of Thermodynamical Equilibrium
- 8 Models
- 9 Equilibrium and Stability: Symmetry and Symmetry Breaking
- 10 Classical Ellipsoids
- 11 Introduction to Dispersive Waves
- 12 Jeans Instability
- PART III Spiral Galaxies
- PART IV Elliptical Galaxies
- PART V In Perspective
- Bibliography
- Index of objects
- Index
11 - Introduction to Dispersive Waves
from PART II - Physical Models
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Contents
- Preface to the Second Edition
- Preface to the First Edition, 2000
- Acknowledgments
- PART I Basic Phenomenology
- PART II Physical Models
- 6 Self-Gravity and Relation to Plasma Physics
- 7 Relaxation Times, Absence of Thermodynamical Equilibrium
- 8 Models
- 9 Equilibrium and Stability: Symmetry and Symmetry Breaking
- 10 Classical Ellipsoids
- 11 Introduction to Dispersive Waves
- 12 Jeans Instability
- PART III Spiral Galaxies
- PART IV Elliptical Galaxies
- PART V In Perspective
- Bibliography
- Index of objects
- Index
Summary
This short introduction to dispersive waves provides an important prerequisite for moving from the dynamics of individual particle orbits to the dynamics of collective effects. As such, the ideas summarized here have a large impact on this book, especially on Part III, in which they are seen at work in the description of density and bending waves. The basic concepts (waves, wave packets, wave trains, group propagation, etc.) define a framework that has found wide and successful applications in hydrodynamics, geophysical fluid dynamics, and plasma physics.
In contrast with the case of hyperbolic waves, for which the description is centered on the properties of one class of partial differential equations, the study of dispersive waves focuses on one characteristic property of the solutions of many different types of dynamical equations that is called the dispersion relation. This is a relation, very often of a rather trivial algebraic form, between space and time modulation of elementary components of the wave process. The relation incorporates the constraints set by the dynamical equations.
It is sometimes believed that the main goal of the dynamicist should be to derive the dispersion relation for a given process and for a given model; the derived expression then would mark the end of the investigation.
- Type
- Chapter
- Information
- Dynamics of Galaxies , pp. 119 - 130Publisher: Cambridge University PressPrint publication year: 2014