80 citations · 847 across the 69 of their papers we have counts for
4 papers · 1 filter
Deformations of plane algebraic curves and integrable systems of hydrodynamic type
Yuji. Kodama, Boris. G. Konopelchenko
We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to…
Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves
Y. Kodama, B. G. Konopelchenko
We discuss the structure of shock singularities of the Burgers-Hopf hierarchy. It is shown that the set of singular solutions defines a stratification of the affine space of the fl…
Quasiconformal Mappings and Solutions of the Dispersionless KP hierarchy
B. Konopelchenko, L. Martinez Alonso, E. Medina
A -formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane…
Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations
B. Konopelchenko, L. Martinez Alonso
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous -equations, is considered. It is shown that the corresponding dynamics, generated b…