Hydrodynamics of Unstable Media  book cover
1st Edition

Hydrodynamics of Unstable Media

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ISBN 9780849328749
Published February 8, 1996 by CRC Press
224 Pages

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Book Description

For the first time, exact analytical solutions are available for some of the most interesting types of problems arising in physics and applied mathematics. Hydrodynamics of Unstable Media outlines the theory of "quasi-gaseous" unstable media, and demonstrates how the theory can be used to obtain analytical solutions. Until now, the solutions to many of the examples considered in this new book have been numerical or partial solutions. By developing a new theory of hydrodynamics for unstable media, the authors provide a means for scientists and mathematicians to solve problems exactly and analytically. Solutions to some 50 problems are provided! Hydrodynamics of Unstable Media features interdisciplinary discussions by internationally recognized authors.

Table of Contents

Quasi-Chaplygin Equations and Their Solutions
The Linear Approximation
Symmetric Self-Similar Solutions
Ellipse-like and Ellipsoid-like Solutions
Three Forms of the Quasi-Chaplygin Equations
General Theory in the One-Dimensional Case
System Reduction to the Laplace Equation
The Evolutionary Selection Principle of Spontaneous Solutions
The Four Simplest Perturbations
Maxima and Minima of Density Profiles
Parametric Representation of the Coordinate
Length-Periodic Perturbations
Hill-Shaped, Well-Shaped, and Wave-Shaped Solitary Perturbations
Elementary Algebraic Solutions
Concerning the Flow Integral and Particle Distribution Functions
A Solution to the General Cauchy Problem
The Media of the Chaplygin Gas Type
The Chaplygin Gas
The Bunemann Plasma Instability
Tearing Instability of Plasma Current Sheet
Parametric Plasma Instability in an External Field
Heating-Radiational Instability of Plasma in an Electric Field
Media of the "Drops on the Ceiling" Type
Overturned Shallow Water
Instability of a Cold Surface Stream in the Ocean
Self-Focusing of Light in a Nonlinear Medium
Modulation Instability of the Langmuir Waves in a Plasma
Self-Contraction of Wave Packets and the Lighthill Criterion
Instability of Waves in Deep Water and Instability of a Gravitating Gas Slab
Separation of an Electron Beam into Bunches
Separation of an Electron Beam into Slabs and Filaments
A Model Mechanism for the Birth of Galaxies
Media with Negative Azimuthal Numbers
Decay of a Liquid Jet into Drops
Plasma Pinch
Gas-Dynamic Particle Acceleration in a Pinch
Electrodynamic Particle Acceleration in a Pinch and Neutrons
Relativistic Plasma Pinch as a Source of Cosmic Rays
Long-Wave Perturbations of Solitons and Solitrons
The Korteweg-de Vries (KdV) Solitons
The Knoidal KdV Waves
Two-Dimensional Solitons of the Kadomtsev-Petviashvili Equation
Solitons of Benjamin-Ono and of Sine-Gordon Equations
Instability of Solitrons of the Generalized KdV Equation
Geometric Optics Approximation for Solitons
Solitons of the Nonlinear Schrödinger Equation (NLSE) and Solitrons of the Generalized NLSE
Energy Principle of Stability in the Theory of Generalized NLSE Solitrons
Nonlinear Description of Hydrodynamic Discontinuity Instabilities
The Tangential Velocity Discontinuity Instability
Problems on TVDI with Bounding Walls
The Corrugation Instability of Shock Waves
Flame Front Instability
An Equation for the Front of Solidification of a Fluid
Stationary Patterns on the Front of Solidification
A Mechanism for Development of Column-like Separateness and "Heaps of Logs" in Rocks
Supplementary Topics in the Theory of Unstable Media
The Chaplygin Problem and Its Solution Method
Inclusion of the Dispersion Corrections to the Chaplygin Media
A List of Equations with the Hilbert Operator
Tables of Formulas and Functions
Short List of Results

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