80 citations · 162 across the 9 of their papers we have counts for
9 papers
SDYM equations on the self-dual background
L. V. Bogdanov
We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the co…
Projective differential geometry of multidimensional dispersionless integrable hierarchies
L. V. Bogdanov, B. G. Konopelchenko
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential -form with the coefficients satisfying the Plücker relatio…
Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
L. V. Bogdanov, B. G. Konopelchenko
Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms of rank N-1 naturally associated with Gr(N-1,…
On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
L. V. Bogdanov
Using Lax-Sato formulation of Manakov-Santini hierarchy, we introduce a class of reductions, such that zero order reduction of this class corresponds to dKP hierarchy, and the firs…
On dispersionless BKP hierarchy and its reductions
L. V. Bogdanov, B. G. Konopelchenko
Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the -function and conformally invariant equations for the dispersio…
Symmetry constraints for real dispersionless Veselov-Novikov equation
Leonid Bogdanov, Boris G. Konopelchenko, Antonio Moro
Symmetry constraints for dispersionless integrable equations are discussed. It is shown that under symmetry constraints the dispersionless Veselov-Novikov equation is reduced to th…
Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser System
L. V. Bogdanov, B. G. Konopelchenko
Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that Möbius symmetry transformation for…
Lattice and q-difference Darboux-Zakharov-Manakov systems via -dressing method
L. V. Bogdanov, B. G. Konopelchenko
A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of -dressing method . Using this scheme, latt…
Generic solutions for some integrable lattice equations
L. V. Bogdanov
We derive the expressions for -functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations.…