59 citations · 107 across the 12 of their papers we have counts for
12 papers
On solutions of the Euler equation for incoherent fluid on a rotating sphere
B. G. Konopelchenko, G. Ortenzi
The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented.…
On Euler equation for incoherent fluid in curved spaces
B. G. Konopelchenko, G. Ortenzi
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated inte…
On pressureless Euler equation with external force
B. G. Konopelchenko, G. Ortenzi
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Eule…
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 blowups of vorticity for the homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Blowups of vorticity for the three- and two- dimensional homogeneous Euler equations are studied. Two regimes of approaching a blowup points, respectively, with variable or fixed t…
Homogeneous Euler equation: blow-ups, gradient catastrophes and singularity of mappings
B. G. Konopelchenko, G. Ortenzi
The paper is devoted to the analysis of the blow-ups of derivatives, gradient catastrophes and dynamics of mappings of associated with the -dimen…
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…
Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems
B. G. Konopelchenko, G. Ortenzi
Changes of type transitions for the two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 X 2 Jordan bloc…
Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian
B. G. Konopelchenko, G. Ortenzi
Cohomological and Poisson structures associated with the special tautological subbundles for the Birkhoff strata of Sato Grassmannian are considered. It is s…
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…