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This book, now in its second edition, introduces the singularity
analysis of differential and difference equations via the Painleve
test and shows how Painleve analysis provides a powerful
algorithmic approach to building explicit solutions to nonlinear
ordinary and partial differential equations. It is illustrated with
integrable equations such as the nonlinear Schroedinger equation,
the Korteweg-de Vries equation, Henon-Heiles type Hamiltonians, and
numerous physically relevant examples such as the
Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov
equation, and mainly the cubic and quintic Ginzburg-Landau
equations. Extensively revised, updated, and expanded, this new
edition includes: recent insights from Nevanlinna theory and
analysis on both the cubic and quintic Ginzburg-Landau equations; a
close look at physical problems involving the sixth Painleve
function; and an overview of new results since the book's original
publication with special focus on finite difference equations. The
book features tutorials, appendices, and comprehensive references,
and will appeal to graduate students and researchers in both
mathematics and the physical sciences.
The Centre de recherches mathCmatiques (CRM) was created in 1968 by
the Universite de Montreal to promote research in the mathematical
sci- ences. It is now a national institute that hosts several
groups, holds special theme years, summer schools, workshops,
postdoctoral program. The focus of its scientific activities ranges
from pure to applied mathematics, and includes satistics,
theoretical computer science, mathematical methods in biology and
life sciences, and mathematical and theoretical physics. The CRM
also promotes collaboration between mathematicians and industry. It
is subsidized by the Natural Sciences and Engineering Research
Council of Canada, the Fonds FCAR od the Province of Quebec, the
Canadian Institute for Advanced Research and has private
endowments. Current ac- tivities, fellowships, and annual reports
can be found on the CRM web page at http://www . CRM. UMontreal.
CAl. The CRM Series in Mathematical Physics will publish
monographs, lec- ture notes, and proceedings base on research
pursued and events held at the Centre de recherches mathematiques.
Yvan Saint-Aubin Montreal Preface The subject of this three-week
school was the explicit integration, that is, analytical as opposed
to numerical, of all kinds of nonlinear differential equations
(ordinary differential, partial differential, finite difference).
The result of such integration is ideally the "general solution,"
but there are numerous physical systems for which only a particular
solution is accessible, for instance the solitary wave of the
equation of Kuramoto and Sivashinsky in turbulence.
This book, now in its second edition, introduces the singularity
analysis of differential and difference equations via the Painleve
test and shows how Painleve analysis provides a powerful
algorithmic approach to building explicit solutions to nonlinear
ordinary and partial differential equations. It is illustrated with
integrable equations such as the nonlinear Schroedinger equation,
the Korteweg-de Vries equation, Henon-Heiles type Hamiltonians, and
numerous physically relevant examples such as the
Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov
equation, and mainly the cubic and quintic Ginzburg-Landau
equations. Extensively revised, updated, and expanded, this new
edition includes: recent insights from Nevanlinna theory and
analysis on both the cubic and quintic Ginzburg-Landau equations; a
close look at physical problems involving the sixth Painleve
function; and an overview of new results since the book's original
publication with special focus on finite difference equations. The
book features tutorials, appendices, and comprehensive references,
and will appeal to graduate students and researchers in both
mathematics and the physical sciences.
Born in 1960 in Newark, New Jersey, Roberts Counts grew up poor in
the projects. Incarcerated at twenty, he began to read everything
he could find from Shakespeare and Malcolm X to Einstein and Robert
Frost. Gradually, he taught himself to write poetry. His poems,
signed Ishmael Shamsid-din-as he was known for almost thirty
years-deal with ghetto violence, the goodness and beauty of nature,
and love as a source of redemption. With wit and lyric energy,
Counts shows us what it takes to resist bitterness and nurture
hope. "These are poems of struggle: with language, in the first
instance; with the mechanisms that spin the universe; with the gods
and goddesses of love; but most of all with a recalcitrant self
which refuses worn and easy paths." -Paul Lauter, Editor, The Heath
Anthology of American Literature
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