75 citations · 163 across the 12 of their papers we have counts for
15 papers
On the Darboux Integrability of the Constant Mean Curvature One Equation for Surfaces in Hyperbolic 3 space
Mark E. Fels, Thomas A. Ivey
We show, using group theoretic constructions, that the system of elliptic partial differential equations whose solutions determine the constant mean curvature immersions into hyper…
The Geometry of Darboux Integrable Elliptic Systems
Mark E. Fels, Thomas A. Ivey
We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system on a…
Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations
Mark E. Fels, Emrullah Yasar
For a scalar evolution equation the cohomology spaces vanishes for while the space $H^{1,2}({\mathc…
Backlund Transformations for Darboux Integrable Differential Systems: Examples and Applications
Ian M. Anderson, Mark E. Fels
In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of Bäcklund transformations. We then showed how this construction can be appl…
On the Construction of Simply Connected Solvable Lie Groups
Mark E. Fels
Let be a Lie algebra valued differential -form on a manifold satisfying the structure equations $d ω_\mathfrak{g} + \frac{1}{2} ω_\mathfrak{g}\wedge ω_\math…
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas
Ian M. Anderson, Mark E. Fels
To every Darboux integrable system there is an associated Lie group which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that…