Articles

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Superposition Formulas for Darboux Integrable Exterior Differential Sys-tems (with Ian M. Anderson and Peter J. Vassiliou), Advances in Mathematics (2009)

In this article we solve an inverse problem in the theory of quotients for differential...

 

Superposition Formulas for Exterior Differential Systems (with I. M. Anderson and P. J. Vassiliou), Advances in Mathematics (2009)
 

Integrating Ordinary Differential Equations with Symmetry Revisited, Foundations of Computational Math (2007)
 

Non-Reductive Four Dimensional Homogeneous Pseudo-Riomannian Mani-Folds (with A. G. Renner), Canadian Journal of Math (2006)
 

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Exterior Differential Systems with Symmetry (with Ian M. Anderson), Acta Applicandae Mathematicae (2005)

We use the theory of reduction of exterior differential systems with symmetry to study the...

 

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The Principle of Symmetric Criticality in General Relativity (with Charles G. Torre), Classical and Quantum Gravity (2002)

We consider a version of Palais' principle of symmetric criticality (PSC) that is applicable to...

 

Transverse Group Action on Bundles (with I. M. Anderson), Topology and Its Applications (2002)
 

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Transverse Group Actions on Bundles (with Ian M. Anderson), Topology and its Applications (2002)

An action of a Lie group G on a bundle is said to be transverse...

 

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Group Invariant Solutions Without Transversality (with Ian M. Anderson and Charles G. Torre), Communications in Mathematical Physics (2000)

We present a generalization of Lie's method for finding the group invariant solutions to a...

 

Group Invariant Solutions without Transversality (with I. M. Anderson and C. G. Torre), Comm. Math. Phys. (2000)
 

Moving Coframes II. Regularization and Theoretical Foundations (with P. J. Olver), Acta. Appl. Math (1999)
 

Moving Coframes I. A Practical Algorithm (with P. J. Olver), Acta. Appl. Math (1998)
 

On Relative Invariants (with P. J. Olver), Mathematische Annalen (1997)
 

Symmetry Reduction of Variational Bicomplexes and the Principle of Symmetric Criticality (with I. M. Anderson), American Journal of Mathematics (1997)
 

Kerr-Schild Rides Again (with A. Held), General Relativity and Gravitation (1989)
 

Contributions to Books

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Transformations of Darboux Integrable Systems (with Ian M. Anderson), Differential equations : geometry, symmetries and integrability : the Abel Symposium 2008, proceedings of the Fifth Abel Symposium, Tromsø, Norway, June 17-22, 2008 Abel Symposia, 2009 (2009)
 

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Group Invariant Solutions in Mathematical Physics and Differential Geometry (with Ian M. Anderson and Charles G. Torre), The Geometrical Study of Differential Equations (2001)

This is a brief overview of our work on the theory of group invariant solutions...

 

Presentations

Superposition Formulas For Exterior Differential Systems, Superposition Formulas For Exterior Differential Systems (2009)
 

On Darboux Integrability, On Darboux Integrability (2007)
 

Darboux Integrability, Darboux Integrability (2006)
 

Differential Geometry wiht Maple, Differential Geometry wiht Maple (2006)
 

Differential Geometry with Maple, Differential Geometry wiht Maple (2006)
 

Exterior Differential Systems with Symmetry I and II, Exterior Differential Systems with Symmetry I and II (2006)
 

Symmetry Reduction of Exterior Differential Systems, Symmetry Reduction of Exterior Differential Systems (2006)
 

A Cochain Map on the G Invariant de Rham Complex, A Cochain Map on the G Invariant de Rham Complex (2004)
 

Non-Reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension 4, Non-Reductivw Homogeneous Pseudo-Riemannian Manifolds of Dimension 4 (2004)
 

Applications of Gauge Transformations to Invariant Variational Problems, Applications of Gauge Transformations to Invariant Variational Problems (1999)
 

The Principle of Symmetric Criticality Without Transversality, The Principle of Symmetric Criticality Without Transversality (1999)
 

The Inverse Problem in the Calculus of Variations, The Inverse Problem in the Calculus of Variations (1997)
 

Symmetry Reduction of Conservation Laws and Variational Principles, Symmetry Reduction of Conservation Laws and Variational Principles (1995)
 

TheGeneralized Inverse Problem in the Calculus of Variations, TheGeneralized Inverse Problem in the Calculus of Variations (1994)
 

The Equivalence Problem for Systems of Second Order Ordinary Differential Equations, The Equivalence Problem for Systems of Second Order Ordinary Differential Equations (1993)