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The Geometrical Study of Differential Equations
 
Edited by: Joshua A. Leslie Howard University, Washington, DC
Thierry P. Robart Howard University, Washington, DC
The Geometrical Study of Differential Equations
Softcover ISBN:  978-0-8218-2964-6
Product Code:  CONM/285
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7875-0
Product Code:  CONM/285.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-2964-6
eBook: ISBN:  978-0-8218-7875-0
Product Code:  CONM/285.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
The Geometrical Study of Differential Equations
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The Geometrical Study of Differential Equations
Edited by: Joshua A. Leslie Howard University, Washington, DC
Thierry P. Robart Howard University, Washington, DC
Softcover ISBN:  978-0-8218-2964-6
Product Code:  CONM/285
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7875-0
Product Code:  CONM/285.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-2964-6
eBook ISBN:  978-0-8218-7875-0
Product Code:  CONM/285.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2852001; 205 pp
    MSC: Primary 17; 20; 22; 34; 35; 39; 51; 53;

    This volume contains papers based on some of the talks given at the NSF-CBMS 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 group-invariant 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 Lie-Bäcklund transformations. The book opens with a modern and illuminating overview of Lie's line-sphere 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.

    Readership

    Graduate students and research mathematicians.

  • Table of Contents
     
     
    • Articles
    • R. Milson — An overview of Lie’s line-sphere 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 differential-difference 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 pseudo-spherical 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 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2852001; 205 pp
MSC: Primary 17; 20; 22; 34; 35; 39; 51; 53;

This volume contains papers based on some of the talks given at the NSF-CBMS 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 group-invariant 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 Lie-Bäcklund transformations. The book opens with a modern and illuminating overview of Lie's line-sphere 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.

Readership

Graduate students and research mathematicians.

  • Articles
  • R. Milson — An overview of Lie’s line-sphere 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 differential-difference 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 pseudo-spherical 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 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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