
Special Issue “Symmetries of Differential Equations: Frames, Invariants and Applications”
The Guest Editors for this special issue are
Niky Kamran (McGill University, Canada)
Gloria Mari Beffa (University of Wisconsin, USA)
Willard Miller (University of Minnesota, USA)
Guillermo R. Sapiro (Duke University, USA)
For over 35 years, Peter Olver has been immensely influential through his research contributions in shaping the development
of a vast area of the mathematical sciences covering the symmetry and integrability properties of differential equations,
Hamiltonian structures and conservation laws for partial differential equations, differential invariants of groups actions,
moving frames, Lie pseudogroups, invariant variational problems, classical invariant theory, computer vision,
invariant numerical algorithms and much more. In each of these areas, Peter has made fundamental discoveries which
have led to new, rich and rapidly growing areas of research. To cite but two instances within this long list,
we mention his epochmaking discovery of recursion operators as structures underlying the integrability of PDEs such
as the KdV equation and his introduction with Mark Fels of the extraordinarily powerful method of equivariant moving
coframes. All of these contributions have been presented through papers written with exemplary clarity, elegance and
readerfriendliness, and books which have rightly become classics thanks to their breadth, clarity and scholarly nature.
Peter has also been a trusted colleague and model mentor to a large number of us within the mathematical community,
always fair and open in his judgment, and always wise in giving the best advice.
We are very happy to dedicate this special issue of SIGMA to him, with great admiration and friendship.
Niky Kamran, Gloria MariBeffa, Willard Miller, Jr., and Guillermo Sapiro
Papers in this Issue:

Invariant Discretization Schemes Using EvolutionProjection Techniques

Alexander Bihlo and JeanChristophe Nave
SIGMA 9 (2013), 052, 23 pages [ abs
pdf ]

Relative Critical Points

Debra Lewis
SIGMA 9 (2013), 038, 28 pages [ abs
pdf ]

On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces

Jeongoo Cheh
SIGMA 9 (2013), 036, 21 pages [ abs
pdf ]

The Symmetry Group of Lamé's System and the Associated Guichard Nets for Conformally Flat Hypersurfaces

João Paulo dos Santos and Keti Tenenblat
SIGMA 9 (2013), 033, 27 pages [ abs
pdf ]

The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis

Mireille Boutin and Shanshan Huang
SIGMA 9 (2013), 031, 25 pages [ abs
pdf ]

Solving Local Equivalence Problems with the Equivariant Moving Frame Method

Francis Valiquette
SIGMA 9 (2013), 029, 43 pages [ abs
pdf ]

GStrands and Peakon Collisions on Diff(R)

Darryl D. Holm and Rossen I. Ivanov
SIGMA 9 (2013), 027, 14 pages [ abs
pdf ]

A QuasiLie Schemes Approach to SecondOrder Gambier Equations

José F. Cariñena, Partha Guha and Javier de Lucas
SIGMA 9 (2013), 026, 23 pages [ abs
pdf ]

Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type

Peter J. Vassiliou
SIGMA 9 (2013), 024, 21 pages [ abs
pdf ]

ObjectImage Correspondence for Algebraic Curves under Projections

Joseph M. Burdis, Irina A. Kogan and Hoon Hong
SIGMA 9 (2013), 023, 31 pages [ abs
pdf ]

Integrable Flows for Starlike Curves in Centroaffine Space

Annalisa Calini, Thomas Ivey and Gloria Marí Beffa
SIGMA 9 (2013), 022, 21 pages [ abs
pdf ]

The Cauchy Problem for Darboux Integrable Systems and NonLinear d'Alembert Formulas

Ian M. Anderson and Mark E. Fels
SIGMA 9 (2013), 017, 22 pages [ abs
pdf ]

Courant Algebroids. A Short History

Yvette KosmannSchwarzbach
SIGMA 9 (2013), 014, 8 pages [ abs
pdf ]

Specialized Orthonormal Frames and Embedding

Frank B. Estabrook
SIGMA 9 (2013), 012, 5 pages [ abs
pdf ]

Invertible Darboux Transformations

Ekaterina Shemyakova
SIGMA 9 (2013), 002, 10 pages [ abs
pdf ]

MultiComponent Integrable Systems and Invariant Curve Flows in Certain Geometries

Changzheng Qu, Junfeng Song and Ruoxia Yao
SIGMA 9 (2013), 001, 19 pages [ abs
pdf ]

Nonlocal Symmetries, Telescopic Vector Fields and λSymmetries of Ordinary Differential Equations

Concepción Muriel and Juan Luis Romero
SIGMA 8 (2012), 106, 21 pages [ abs
pdf ]

The KleinGordon Equation and Differential Substitutions of the Form v=φ(u,u_{x},u_{y})

Mariya N. Kuznetsova, Aslı Pekcan and Anatoliy V. Zhiber
SIGMA 8 (2012), 090, 37 pages [ abs
pdf ]

Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables

Philip Broadbridge, Claudia M. Chanu and Willard Miller Jr.
SIGMA 8 (2012), 089, 31 pages [ abs
pdf ]

Sylvester versus Gundelfinger

Andries E. Brouwer and Mihaela Popoviciu
SIGMA 8 (2012), 075, 7 pages [ abs
pdf ]

Motions of Curves in the Projective Plane Inducing the KaupKupershmidt Hierarchy

Emilio Musso
SIGMA 8 (2012), 030, 20 pages [ abs
pdf ]

Lagrange Anchor and Characteristic Symmetries of Free Massless Fields

Dmitry S. Kaparulin, Simon L. Lyakhovich and Alexey A. Sharapov
SIGMA 8 (2012), 021, 18 pages [ abs
pdf ]

