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Product Code:  CONM/285 
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Book DetailsContemporary MathematicsVolume: 285; 2001; 205 ppMSC: Primary 17; 20; 22; 34; 35; 39; 51; 53;
This volume contains papers based on some of the talks given at the NSFCBMS conference on “The Geometrical Study of Differential Equations” held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a groupinvariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex for the calculus of difference equations and an original structural investigation of LieBäcklund transformations. The book opens with a modern and illuminating overview of Lie's linesphere correspondence and concludes with several interesting open problems arising from symmetry analysis of PDEs. It offers a rich source of inspiration for new or established researchers in the field.
This book can serve nicely as a companion volume to Selected Topics in the Geometrical Study of Differential Equations, by Niky Kamran, in the AMS series, CBMS Regional Conference Series in Mathematics.ReadershipGraduate students and research mathematicians.

Table of Contents

Articles

R. Milson  An overview of Lie’s linesphere correspondence [ MR 1874301 ]

V. Torrisi and M. C. Nucci  Application of Lie group analysis to a mathematical model which describes HIV transmission [ MR 1874284 ]

Richard Beals  Geometry and PDE on the Heisenberg group: a case study [ MR 1874285 ]

G. Marí Beffa  Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems [ MR 1874286 ]

Barbara A. Shipman  On the fixed points of the Toda hierarchy [ MR 1874287 ]

I. M. Anderson, M. E. Fels and C. G. Torre  Group invariant solutions in mathematical physics and differential geometry [ MR 1874288 ]

P. E. Hydon  Discrete symmetries of differential equations [ MR 1874289 ]

Thomas A. Ivey  Integrable geometric evolution equations for curves [ MR 1874290 ]

Jan A. Sanders and Jing Ping Wang  On integrability of evolution equations and representation theory [ MR 1874291 ]

Michael Oberguggenberger  Symmetry groups, nonlinear partial differential equations, and generalized functions [ MR 1874292 ]

R. Hernández Heredero  Lie symmetries of differentialdifference equations [ MR 1874293 ]

Elizabeth L. Mansfield and Peter E. Hydon  On a variational complex for difference equations [ MR 1874294 ]

Irina A. Kogan and Peter J. Olver  The invariant variational bicomplex [ MR 1874295 ]

Enrique G. Reyes  On geometrically integrable equations and hierarchies of pseudospherical type [ MR 1874296 ]

Irina A. Kogan  Inductive construction of moving frames [ MR 1874297 ]

Vladimir Itskov  Orbit reduction of contact ideals [ MR 1874298 ]

Thierry Robart  About the local and formal geometry of PDE [ MR 1874299 ]

Peter A. Clarkson and Elizabeth L. Mansfield  Open problems in symmetry analysis [ MR 1874300 ]


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This volume contains papers based on some of the talks given at the NSFCBMS conference on “The Geometrical Study of Differential Equations” held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a groupinvariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex for the calculus of difference equations and an original structural investigation of LieBäcklund transformations. The book opens with a modern and illuminating overview of Lie's linesphere correspondence and concludes with several interesting open problems arising from symmetry analysis of PDEs. It offers a rich source of inspiration for new or established researchers in the field.
This book can serve nicely as a companion volume to Selected Topics in the Geometrical Study of Differential Equations, by Niky Kamran, in the AMS series, CBMS Regional Conference Series in Mathematics.
Graduate students and research mathematicians.

Articles

R. Milson  An overview of Lie’s linesphere correspondence [ MR 1874301 ]

V. Torrisi and M. C. Nucci  Application of Lie group analysis to a mathematical model which describes HIV transmission [ MR 1874284 ]

Richard Beals  Geometry and PDE on the Heisenberg group: a case study [ MR 1874285 ]

G. Marí Beffa  Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems [ MR 1874286 ]

Barbara A. Shipman  On the fixed points of the Toda hierarchy [ MR 1874287 ]

I. M. Anderson, M. E. Fels and C. G. Torre  Group invariant solutions in mathematical physics and differential geometry [ MR 1874288 ]

P. E. Hydon  Discrete symmetries of differential equations [ MR 1874289 ]

Thomas A. Ivey  Integrable geometric evolution equations for curves [ MR 1874290 ]

Jan A. Sanders and Jing Ping Wang  On integrability of evolution equations and representation theory [ MR 1874291 ]

Michael Oberguggenberger  Symmetry groups, nonlinear partial differential equations, and generalized functions [ MR 1874292 ]

R. Hernández Heredero  Lie symmetries of differentialdifference equations [ MR 1874293 ]

Elizabeth L. Mansfield and Peter E. Hydon  On a variational complex for difference equations [ MR 1874294 ]

Irina A. Kogan and Peter J. Olver  The invariant variational bicomplex [ MR 1874295 ]

Enrique G. Reyes  On geometrically integrable equations and hierarchies of pseudospherical type [ MR 1874296 ]

Irina A. Kogan  Inductive construction of moving frames [ MR 1874297 ]

Vladimir Itskov  Orbit reduction of contact ideals [ MR 1874298 ]

Thierry Robart  About the local and formal geometry of PDE [ MR 1874299 ]

Peter A. Clarkson and Elizabeth L. Mansfield  Open problems in symmetry analysis [ MR 1874300 ]