Solvable Symmetry Structures in Differential Form Applications

We investigate symmetry techniques for expressing various exterior differential forms in terms of simplified coordinate systems. In particular, we give extensions of the Lie symmetry approach to integrating Frobenius integrable distributions based on a solvable structure of symmetries and show how a solvable structure of symmetries may be used to find local coordinates for the Pfaffian problem and Darboux's theorem.