|
Showing 1 - 6 of
6 matches in All Departments
This book on integrable systems and symmetries presents new results
on applications of symmetries and integrability techniques to the
case of equations defined on the lattice. This relatively new field
has many applications, for example, in describing the evolution of
crystals and molecular systems defined on lattices, and in finding
numerical approximations for differential equations preserving
their symmetries. The book contains three chapters and five
appendices. The first chapter is an introduction to the general
ideas about symmetries, lattices, differential difference and
partial difference equations and Lie point symmetries defined on
them. Chapter 2 deals with integrable and linearizable systems in
two dimensions. The authors start from the prototype of integrable
and linearizable partial differential equations, the Korteweg de
Vries and the Burgers equations. Then they consider the best known
integrable differential difference and partial difference
equations. Chapter 3 considers generalized symmetries and conserved
densities as integrability criteria. The appendices provide details
which may help the readers' understanding of the subjects presented
in Chapters 2 and 3. This book is written for PhD students and
early researchers, both in theoretical physics and in applied
mathematics, who are interested in the study of symmetries and
integrability of difference equations.
This book shows how Lie group and integrability techniques,
originally developed for differential equations, have been adapted
to the case of difference equations. Difference equations are
playing an increasingly important role in the natural sciences.
Indeed, many phenomena are inherently discrete and thus naturally
described by difference equations. More fundamentally, in subatomic
physics, space-time may actually be discrete. Differential
equations would then just be approximations of more basic discrete
ones. Moreover, when using differential equations to analyze
continuous processes, it is often necessary to resort to numerical
methods. This always involves a discretization of the differential
equations involved, thus replacing them by difference ones. Each of
the nine peer-reviewed chapters in this volume serves as a
self-contained treatment of a topic, containing introductory
material as well as the latest research results and exercises. Each
chapter is presented by one or more early career researchers in the
specific field of their expertise and, in turn, written for early
career researchers. As a survey of the current state of the art,
this book will serve as a valuable reference and is particularly
well suited as an introduction to the field of symmetries and
integrability of difference equations. Therefore, the book will be
welcomed by advanced undergraduate and graduate students as well as
by more advanced researchers.
The NATO Advanced Research Workshop "Painleve Transcendents, their
Asymp totics and Physical Applications," held at the Alpine Inn in
Sainte-Adele, near Montreal, September 2 -7, 1990, brought together
a group of experts to discuss the topic and produce this volume.
There were 41 participants from 14 countries and 27 lectures were
presented, all included in this volume. The speakers presented
reviews of topics to which they themselves have made important
contributions and also re sults of new original research. The
result is a volume which, though multiauthored, has the character
of a monograph on a single topic. This is the theory of nonlinear
ordinary differential equations, the solutions of which have no
movable singularities, other than poles, and the extension of this
theory to partial differential equations. For short we shall call
such systems "equations with the Painleve property." The search for
such equations was a very topical mathematical problem in the 19th
century. Early work concentrated on first order differential
equations. One of Painleve's important contributions in this field
was to develop simple methods applicable to higher order equations.
In particular these methods made possible a complete analysis of
the equation;; = f(y', y, x), where f is a rational function of y'
and y, with coefficients that are analytic in x. The fundamental
result due to Painleve (Acta Math."
The NATO Advanced Research Workshop "Painleve Transcendents, their
Asymp totics and Physical Applications," held at the Alpine Inn in
Sainte-Adele, near Montreal, September 2 -7, 1990, brought together
a group of experts to discuss the topic and produce this volume.
There were 41 participants from 14 countries and 27 lectures were
presented, all included in this volume. The speakers presented
reviews of topics to which they themselves have made important
contributions and also re sults of new original research. The
result is a volume which, though multiauthored, has the character
of a monograph on a single topic. This is the theory of nonlinear
ordinary differential equations, the solutions of which have no
movable singularities, other than poles, and the extension of this
theory to partial differential equations. For short we shall call
such systems "equations with the Painleve property." The search for
such equations was a very topical mathematical problem in the 19th
century. Early work concentrated on first order differential
equations. One of Painleve's important contributions in this field
was to develop simple methods applicable to higher order equations.
In particular these methods made possible a complete analysis of
the equation;; = f(y', y, x), where f is a rational function of y'
and y, with coefficients that are analytic in x. The fundamental
result due to Painleve (Acta Math."
This book shows how Lie group and integrability techniques,
originally developed for differential equations, have been adapted
to the case of difference equations. Difference equations are
playing an increasingly important role in the natural sciences.
Indeed, many phenomena are inherently discrete and thus naturally
described by difference equations. More fundamentally, in subatomic
physics, space-time may actually be discrete. Differential
equations would then just be approximations of more basic discrete
ones. Moreover, when using differential equations to analyze
continuous processes, it is often necessary to resort to numerical
methods. This always involves a discretization of the differential
equations involved, thus replacing them by difference ones. Each of
the nine peer-reviewed chapters in this volume serves as a
self-contained treatment of a topic, containing introductory
material as well as the latest research results and exercises. Each
chapter is presented by one or more early career researchers in the
specific field of their expertise and, in turn, written for early
career researchers. As a survey of the current state of the art,
this book will serve as a valuable reference and is particularly
well suited as an introduction to the field of symmetries and
integrability of difference equations. Therefore, the book will be
welcomed by advanced undergraduate and graduate students as well as
by more advanced researchers.
Difference equations are playing an increasingly important role in
the natural sciences. Indeed many phenomena are inherently discrete
and are naturally described by difference equations. Phenomena
described by differential equations are therefore approximations of
more basic discrete ones. Moreover, in their study it is very often
necessary to resort to numerical methods. This always involves a
discretization of the differential equations involved, thus
replacing them by difference equations. This book shows how Lie
group and integrability techniques, originally developed for
differential equations, have been adapted to the case of difference
ones. Each of the eleven chapters is a self-contained treatment of
a topic, containing introductory material as well as the latest
research results. The book will be welcomed by graduate students
and researchers seeking an introduction to the field. As a survey
of the current state of the art it will also serve as a valuable
reference.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|