16 citations · 16 across the 4 of their papers we have counts for
4 papers
The Geodesics of Rolling Ball Systems
Daniel R. Cole
A well-known and interesting family of sub-Riemannian space are the systems involving two balls rolling against each other without slipping or twisting. In this note, we show how t…
Periodic Solutions and Rogue Wave Type Extended Compactons in the Nonlinear Schrodinger Equation and ϕ^{4} Theories
Patrick Johnson, Daniel Cole, Zohar Nussinov
By employing a mapping to classical anharmonic oscillators, we explore a class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1 dimensions and, by extension, asympt…
A Natural Connection on (2,3) Sub-Riemannian Manifolds
Daniel R. Cole
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties o…
C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable
Daniel R. Cole, Scott D. Pauls
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable,…