The Geometrical Study of Differential Equations: NSF-CBMS Conference on the Geometrical Study of Differential Equations, June 20-25, 2000, Howard University, Washington, D.C.(Contemporary Mathematics)

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-Backlund 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"".

Table of Contents:
An overview of Lie's line-sphere correspondence by R. Milson Application of Lie group analysis to a mathematical model which describes HIV transmission by V. Torrisi and M. C. Nucci Geometry and PDE on the Heisenberg group: A case study by R. Beals Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems by G. Mari Beffa On the fixed points of the toda hierarchy by B. A. Shipman Group invariant solutions in mathematical physics and differential geometry by I. M. Anderson, M. E. Fels, and C. G. Torre Discrete symmetries of differential equations by P. E. Hydon Integrable geometric evolution equations for curves by T. A. Ivey On integrability of evolution equations and representation theory by J. A. Sanders and J. P. Wang Symmetry groups, nonlinear partial differential equations, and generalized functions by M. Oberguggenberger Lie symmetries of differential-difference equations by R. H. Heredero On a variational complex for difference equations by E. L. Mansfield and P. E. Hydon The invariant variational bicomplex by I. A. Kogan and P. J. Olver On geometrically integrable equations and hierarchies of pseudo-spherical type by E. G. Reyes Inductive construction of moving frames by I. A. Kogan Orbit reduction of contact ideals and group-invariant variational problems by V. Itskov About the local and formal geometry of PDE by T. Robart Open problems in symmetry analysis by P. A. Clarkson and E. L. Mansfield.