30 citations · 30 across the 4 of their papers we have counts for
4 papers
Schwarz Reflection Geometry I: Continuous Iteration of Reflection
Annalisa Calini, Joel Langer
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensiona…
Localized induction equation, Heisenberg chain, and nonlinear Schrodinger equation
Joel Langer, Ron Perline
The three equations named in the title are examples of infinite-dimensional completely integrable Hamiltonian systems, and are related to each other via simple geometric constructi…
The planar filament equation
Joel Langer, Ron Perline
The planar filament equation and its relation to the modified Korteweg-deVries equation are studied in the context of Poisson geometry. The structure of the planar filament equatio…
Local Geometric Invariants of Integrable Evolution Equations
Joel Langer, Ron Perline
The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families o…