96 citations · 279 across the 13 of their papers we have counts for
13 papers
On an integrable 2+1-dimensional extended Dym equation: Lax pair, -dressing scheme and modulation
Boris Konopelchenko, Colin Rogers, Pablo Amster
In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon soli…
Tropical Limit in Statistical Physics
M. Angelelli, B. Konopelchenko
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adap…
Critical points, Lauricella functions and Whitham-type equations
Y. Kodama, B. Konopelchenko, W. K. Schief
A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darbo…
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,…
Singular sectors of the 1-layer Benney and dToda systems and their interrelations
B. Konopelchenko, L. Martinez Alonso, E. Medina
Complete description of the singular sectors of the 1-layer Benney system (classical long wave equation) and dToda system is presented. Associated Euler-Poisson-Darboux equations E…
On the singular sector of the Hermitian random matrix model in the large N limit
B. Konopelchenko, L. Martinez Alonso, E. Medina
The singular sector of zero genus case for the Hermitian random matrix model in the large N limit is analyzed. It is proved that the singular sector of the hodograph solutions for…
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
B. Konopelchenko, L. Martinez Alonso, E. Medina
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the…
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…
Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
B. Konopelchenko, L. Martinez Alonso
The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hie…
Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy
L. V. Bogdanov, B. G. Konopelchenko
Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This…
Generalized Weierstrass formulae, soliton equations and Willmore surfaces. I. Tori of revolution and the mKdV equation
B. G. Konopelchenko, I. A. Taimanov
A new approach is proposed for study structure and properties of the total squared mean curvature of surfaces in . It is based on the generalized Weierstrass formula…
Constant mean curvature surfaces via integrable dynamical system
B. G. Konopelchenko, I. A. Taimanov
It is shown that the equation which describes constant mean curvature surface via the generalized Weierstrass-Enneper inducing has Hamiltonian form. Its simplest finite-dimensional…