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In the past few years there has been a fruitful exchange of
expertise on the subject of partial differential equations (PDEs)
between mathematicians from the People's Republic of China and the
rest of the world. The goal of this collection of papers is to
summarize and introduce the historical progress of the development
of PDEs in China from the 1950s to the 1980s. The results presented
here were mainly published before the 1980s, but, having been
printed in the Chinese language, have not reached the wider
audience they deserve. Topics covered include, among others,
nonlinear hyperbolic equations, nonlinear elliptic equations,
nonlinear parabolic equations, mixed equations, free boundary
problems, minimal surfaces in Riemannian manifolds, microlocal
analysis and solitons. For mathematicians and physicists interested
in the historical development of PDEs in the People's Republic of
China.
Soliton theory is an important branch of applied mathematics and
mathematical physics. An active and productive field of research,
it has important applications in fluid mechanics, nonlinear optics,
classical and quantum fields theories etc. This book presents a
broad view of soliton theory. It gives an expository survey of the
most basic ideas and methods, such as physical background, inverse
scattering, Backl nd transformations, finite-dimensional completely
integrable systems, symmetry, Kac-moody algebra, solitons and
differential geometry, numerical analysis for nonlinear waves, and
gravitational solitons. Besides the essential points of the theory,
several applications are sketched and some recent developments,
partly by the authors and their collaborators, are presented.
GU Chaohao The soliton theory is an important branch of nonlinear
science. On one hand, it describes various kinds of stable motions
appearing in - ture, such as solitary water wave, solitary signals
in optical ?bre etc., and has many applications in science and
technology (like optical signal communication). On the other hand,
it gives many e?ective methods ofgetting explicit solutions of
nonlinear partial di?erential equations. Therefore, it has
attracted much attention from physicists as well as mathematicians.
Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems.
Getting explicit solutions is usually a di?cult task. Only in c-
tain special cases can the solutions be written down explicitly.
However, for many soliton equations, people have found quite a few
methods to get explicit solutions. The most famous ones are the
inverse scattering method, B] acklund transformation etc.. The
inverse scattering method is based on the spectral theory of
ordinary di?erential equations. The
Cauchyproblemofmanysolitonequationscanbetransformedtosolving a
system of linear integral equations. Explicit solutions can be
derived when the kernel of the integral equation is degenerate. The
B] ac ] klund transformation gives a new solution from a known
solution by solving a system of completely integrable partial
di?erential equations. Some complicated "nonlinear superposition
formula" arise to substitute the superposition principlein linear
science."
GU Chaohao The soliton theory is an important branch of nonlinear
science. On one hand, it describes various kinds of stable motions
appearing in - ture, such as solitary water wave, solitary signals
in optical ?bre etc., and has many applications in science and
technology (like optical signal communication). On the other hand,
it gives many e?ective methods ofgetting explicit solutions of
nonlinear partial di?erential equations. Therefore, it has
attracted much attention from physicists as well as mathematicians.
Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems.
Getting explicit solutions is usually a di?cult task. Only in c-
tain special cases can the solutions be written down explicitly.
However, for many soliton equations, people have found quite a few
methods to get explicit solutions. The most famous ones are the
inverse scattering method, B] acklund transformation etc.. The
inverse scattering method is based on the spectral theory of
ordinary di?erential equations. The
Cauchyproblemofmanysolitonequationscanbetransformedtosolving a
system of linear integral equations. Explicit solutions can be
derived when the kernel of the integral equation is degenerate. The
B] ac ] klund transformation gives a new solution from a known
solution by solving a system of completely integrable partial
di?erential equations. Some complicated "nonlinear superposition
formula" arise to substitute the superposition principlein linear
science."
Soliton theory is an important branch of applied mathematics and
mathematical physics. An active and productive field of research,
it has important applications in fluid mechanics, nonlinear optics,
classical and quantum fields theories etc. This book presents a
broad view of soliton theory. It gives an expository survey of the
most basic ideas and methods, such as physical background, inverse
scattering, Backl nd transformations, finite-dimensional completely
integrable systems, symmetry, Kac-moody algebra, solitons and
differential geometry, numerical analysis for nonlinear waves, and
gravitational solitons. Besides the essential points of the theory,
several applications are sketched and some recent developments,
partly by the authors and their collaborators, are presented.
These refereed proceedings present recent developments on specific
mathematical and physical aspects of nonlinear dynamics. The new
findings discussed in here will be equally useful to graduate
students and researchers. The topics dealt with cover a wide range
of phenomena: solitons, integrable systems, Hamiltonian structures,
Backlund and Darboux transformation, symmetries, fi-
nite-dimensional dynamical systems, quantum and statistical
mechanics, knot theory and braid group, R-matrix method, Hirota and
Painleve analysis, and applications to water waves, lattices,
porous media, string theory and even cellular automata.
The DD6 Symposium was, like its predecessors DD1 to DD5 both a
research symposium and a summer seminar and concentrated on
differential geometry. This volume contains a selection of the
invited papers and some additional contributions. They cover recent
advances and principal trends in current research in differential
geometry.
In the past few years there has been a fruitful exchange of
expertise on the subject of partial differential equations (PDEs)
between mathematicians from the People's Republic of China and the
rest of the world. The goal of this collection of papers is to
summarize and introduce the historical progress of the development
of PDEs in China from the 1950s to the 1980s. The results presented
here were mainly published before the 1980s, but, having been
printed in the Chinese language, have not reached a wider audience.
Topics covered include, among others, nonlinear hyperbolic
equations, nonlinear elliptic equations, nonlinear parabolic
equations, mixed equations, free boundary problems, minimal
surfaces in Riemannian manifolds, microlocal analysis and solitons.
The text is suitable for mathematicians and physicists interested
in the historical development of PDEs in the People's Republic of
China.
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