59 citations · 107 across the 12 of their papers we have counts for
5 papers · 1 filter
Affine manifolds: The differential geometry of the multi-dimensionally consistent TED equation
W. K. Schief, U. Hertrich-Jeromin, B. G. Konopelchenko
It is shown that a canonical geometric setting of the integrable TED equation is a Kahlerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of t…
On universality of homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions pr…
Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates
B. G. Konopelchenko, W. K. Schief, A. Szereszewski
Eigenfunctions are shown to constitute privileged coordinates of self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. T…
Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
B. G. Konopelchenko, G. Ortenzi
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic syst…
Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
B. G. Konopelchenko, W. K. Schief
It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarc…