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On the occasion of the 150th anniversary of Sophus Lie, an
International Work shop "Modern Group Analysis: advanced analytical
and computational methods in mathematical physics" has been
organized in Acireale (Catania, Sicily, October 27 31, 1992). The
Workshop was aimed to enlighten the present state ofthis rapidly
expanding branch of applied mathematics. Main topics of the
Conference were: * classical Lie groups applied for constructing
invariant solutions and conservation laws; * conditional (partial)
symmetries; * Backlund transformations; * approximate symmetries; *
group analysis of finite-difference equations; * problems of group
classification; * software packages in group analysis. The success
of the Workshop was due to the participation of many experts in
Group Analysis from different countries. This book consists of
selected papers presented at the Workshop. We would like to thank
the Scientific Committee for the generous support of recommending
invited lectures and selecting the papers for this volume, as well
as the members of the Organizing Committee for their help. The
Workshop was made possible by the financial support of several
sponsors that are listed below. It is also a pleasure to thank our
colleague Enrico Gregorio for his invaluable help of this volume.
Approach your problems from the right It isn't that they can't see
the solution. end and begin with the answers. Then It is that they
can't see the problem. one day, perhaps you will find the final
question. G.K. Chesterton. The Scandal of Father Brown 'The Point
of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The
Chinese Maze Murders. Growing specialization and diversification
have brought a host of monographs and textbooks on increasingly
specialized topics. However, the "tree" of knowledge of mathematics
and related fields does not grow only by putting forth new
branches. It also happens, quite often in fact, that branches which
were thought to be completely disparate are suddenly seen to be
related. Further, the kind and level of sophistication of
mathematics applied in various sciences has changed drastically in
recent years: measure theory is used (non-trivially) in - gional
and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of
water meet one another in pack ing and covering theory; quantum
fields, crystal defects and mathematical programming profit from
homotopy theory; Lie algebras are relevant to filtering; and
prediction and electrical engineering can use Stein spaces. And in
addition to this there are such new emerging subdisciplines as
"completely integrable systems," "chaos, synergetics and
large-scale order," which are almost impossible to fit into the
existing classification schemes. They draw upon widely different
sections of mathematics."
On the occasion of the 150th anniversary of Sophus Lie, an
International Work shop "Modern Group Analysis: advanced analytical
and computational methods in mathematical physics" has been
organized in Acireale (Catania, Sicily, October 27 31, 1992). The
Workshop was aimed to enlighten the present state ofthis rapidly
expanding branch of applied mathematics. Main topics of the
Conference were: * classical Lie groups applied for constructing
invariant solutions and conservation laws; * conditional (partial)
symmetries; * Backlund transformations; * approximate symmetries; *
group analysis of finite-difference equations; * problems of group
classification; * software packages in group analysis. The success
of the Workshop was due to the participation of many experts in
Group Analysis from different countries. This book consists of
selected papers presented at the Workshop. We would like to thank
the Scientific Committee for the generous support of recommending
invited lectures and selecting the papers for this volume, as well
as the members of the Organizing Committee for their help. The
Workshop was made possible by the financial support of several
sponsors that are listed below. It is also a pleasure to thank our
colleague Enrico Gregorio for his invaluable help of this volume.
Approach your problems from the right It isn't that they can't see
the solution. end and begin with the answers. Then It is that they
can't see the problem. one day, perhaps you will find the final
question. G.K. Chesterton. The Scandal of Father Brown 'The Point
of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The
Chinese Maze Murders. Growing specialization and diversification
have brought a host of monographs and textbooks on increasingly
specialized topics. However, the "tree" of knowledge of mathematics
and related fields does not grow only by putting forth new
branches. It also happens, quite often in fact, that branches which
were thought to be completely disparate are suddenly seen to be
related. Further, the kind and level of sophistication of
mathematics applied in various sciences has changed drastically in
recent years: measure theory is used (non-trivially) in - gional
and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of
water meet one another in pack ing and covering theory; quantum
fields, crystal defects and mathematical programming profit from
homotopy theory; Lie algebras are relevant to filtering; and
prediction and electrical engineering can use Stein spaces. And in
addition to this there are such new emerging subdisciplines as
"completely integrable systems," "chaos, synergetics and
large-scale order," which are almost impossible to fit into the
existing classification schemes. They draw upon widely different
sections of mathematics."
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie’s striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. - This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory
- Includes a concise and self contained introduction to differential equations
- Easy to follow and comprehensive introduction to Lie group analysis
- The methods described in this book have many applications
The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.
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