5 papers
On a class of three-dimensional integrable Lagrangians
E. V. Ferapontov, K. R. Khusnutdinova, S. P. Tsarev
We characterize non-degenerate Lagrangians of the form such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})…
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…
The analogue of Wilczynski's projective frame in Lie sphere geometry: Lie-applicable surfaces and commuting Schrödinger operators with magnetic fields
E. V. Ferapontov
We propose a twistor construction of surfaces in Lie sphere geometry based on the linear system which copies equations of Wilczynski's projective frame. In the particular case of L…
Integrable systems in projective differential geometry
E. V. Ferapontov
Some of the most important classes of surfaces in projective 3-space are reviewed: these are isothermally asymptotic surfaces, projectively applicable surfaces, surfaces of Jonas,…
Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry
E. V. Ferapontov
It is demonstrated that the stationary Veselov-Novikov (VN) and the stationary modified Veselov-Novikov (mVN) equations describe one and the same class of surfaces in projective di…