книги / Нестационарные структуры и диффузионный хаос

CHAOS AND DISSIPATIVE

STRUCTURES

IN 'REACTION-DIFFUSION' SYSTEMS.

Akhromeyeva

T.S.,

Kurdyumov

S.P.,

Malinetskii

G.G.,

Samarskii

A.A.

The

book

is

written by

the

leading

Soviet

specialists

in

the

field

of

mathematical

physics

and

synergetics.

One

of its authors Aqad. Samarskii A.A. is

the

creator

of

the

Soviet

largest

scientific

school

in

computational

and

mathematical

physics.

Scientific

results

received

by

this

school

have acquired worldwide recognition.

The books by Acad. Samarskii have been

repeatedly

publiwshed in many countries. At

the

present

time

Acad

Samarskiiis

the

Chairman

of

the

National Committee

on

Mathematical

Modelling.

Another

author,

Corresponding

Member

of

the

USSR

Academy

of

Sciences,

Director

of

Keldysh

Institute

of

Applied

Mathematics

Kurdyumov

S.P.

is

a

recognised

authority

in

synergetics.

The

basis

of

the

book

is the

survey

'Nonstationary

Struct ires

and

Diffusion-induced

chaos

in

Nonlinear

Media'

which

was

published

in

the

journal

'Physics

Reports’

in

1989.

The

book describes

a new

direction

in synergetics

-

that of the theory of nonstationary

localised

dissipative

structures.

This

is

a

new type

of

ordering

that

occur

in

the

systems

with

a

positive

feedback.

Much

consideration

is

given

to

the

main

mathematical

results, new

methods of

1he

analysis

of

the

systems

under

study,

and

applications

to

the

tasks

of

chemical

kinetics,

plasma

physics,

quantum

field

theory.

Another

theme

of

the

book

is

the

analysis

of

time-dependent

generalized

Ginzburg-Landau

(TDGL)

equation,

which

is

one

of the

main

models of

synergetics.

For

its

investigation,

in

recent

years

scientists

have

used

methods

of

invariant—group

analysis,

the

theory

of

dynamical

systems

with

continious

time,

the

theory

of

one-dimensional and two-dimensional

maps,

and

theory

of

inertial

manifolds.

The

book

gives

a

detailed

consideration

to

the

hierarchy

of

simplified

models

built

when analysing

TDGL.

The provement of equivalence of

this

equation

to

some

dynamical

system

(inertial

form)

is

a

key

result

in

applied

mathematics

in

recent

years.

This

direction

of

investigation is being analised in the book as well.

The

book

is

well

illustrated.

The

rigorous

results

being

discussed

in

the

book

are

supported

by

many

examples

from

various

sciences.

The

book

may

be

interesting

for

specialists

in

applied

mathematics,

"

for

chemists,

physicists,

biologists. It

may

also

find

wide

readership

among

people

taking

interest

in

synergetics.

The

book

contains

not

only

the original

results

achieved

by

the authors,

but also

the

analysis

of the main concepts of nonlinear

dynamics,

which

makes

it

useful

for

many

post-graduates.