3 papers
math.DG2008
On implicit ODEs with hexagonal web of solutions
S. I. Agafonov
Solutions of an implicit ODE form a web. Already for cubic ODEs the 3-web of solutions has a nontrivial local invariant, namely the curvature form. Thus any local classification of…
nlin.SI2001
Discrete : embedded circle patterns with the combinatorics of the square grid and discrete Painlevé equations
S. I. Agafonov
A discrete analog of the holomorphic map is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding cir…
math.DG2001
Systems of conservation laws of Temple class, equations of associativity and linear congruences in projective space
S. I. Agafonov, E. V. Ferapontov
We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective sp…