80 citations · 847 across the 69 of their papers we have counts for
69 papers
On the fine structure and hierarchy of gradient catastrophes for multidimensional homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Blow-ups of derivatives and gradient catastrophes for the -dimensional homogeneous Euler equation are discussed. It is shown that, in the case of generic initial data, the blow-…
Integrability properties of symmetric 4+4-dimensional heavenly type equation
L. V. Bogdanov, B. G. Konopelchenko
We demonstrate that the dispersionless -dressing method developed before for general heavenly equation is applicable to the and - dimensional symmetric…
Entropy driven transformations of statistical hypersurfaces
Mario Angelelli, Boris Konopelchenko
Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are cons…
On the plane into plane mappings of hydrodynamic type. Parabolic case
B. G. Konopelchenko, G. Ortenzi
Singularities of plane into plane mappings described by parabolic two-component systems of quasi-liner partial differential equations of the first order are studied. Impediments ar…
On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation
B. G. Konopelchenko, W. K. Schief
Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n+2n-dimensional integrable partial…
Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain
B. G. Konopelchenko, G. Ortenzi
Non-standard parabolic regularization of gradient catastrophes for the Burgers-Hopf equation is proposed. It is based on the analysis of all (generic and higher order) gradient cat…