Hydrodynamics of Unstable Media: 1st Edition (Hardback) book cover

Hydrodynamics of Unstable Media

1st Edition

By Boris A. Trubnikov, Sergey K. Zhdanov, Sergei M. Zverev

CRC Press

224 pages

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Hardback: 9780849328749
pub: 1996-02-08
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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

Introduction

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

Bibliography

Index

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
SCI055000
SCIENCE / Physics