49 citations · 105 across the 22 of their papers we have counts for
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Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and Seiberg-Witten theories
Vladimir Dragović, Vasilisa Shramchenko
We introduce the dynamics of Toda curves of order and derive differential equations governing this dynamics. We apply the obtained results to describe isoperiodic deformations…
Deformations of the Hill curves and isoperiodicity in the KdV and the sine-Gordon equations
Vladimir Dragovic, Vasilisa Shramchenko
We consider a family of genus hyperelliptic curves as double ramified coverings over the Riemann sphere with the set of branch points of the form $\{0, \infty, x_1, \dots, x_g,…
Isoperiodic deformations of Abelian differentials of the second kind over elliptic curves and the Boussinesq equation
Vladimir Dragović, Vasilisa Shramchenko
We study deformations of a genus one Riemann surface and of a second order Abelian differential on the surface which preserve the periods of the differential with respect to a chos…
Isoharmonic deformations and constrained Schlesinger systems
Vladimir Dragović, Vasilisa Shramchenko
We introduce and study the dynamics of Chebyshev polynomials on real intervals. We define isoharmonic deformations as a natural generalization of the Chebyshev dynamics. This…
Note on algebro-geometric solutions to triangular Schlesinger systems
Vladimir Dragovic, Vasilisa Shramchenko
We construct algebro-geometric upper triangular solutions of rank two Schlesinger systems. Using these solutions we derive two families of solutions to the sixth Painlevé equation…
Algebro-geometric solutions of the Schlesinger systems and the Poncelet-type polygons in higher dimensions
Vladimir Dragovic, Vasilisa Shramchenko
A new method to construct algebro-geometric solutions of rank two Schlesinger systems is presented. For an elliptic curve represented as a ramified double covering of CP^1, a merom…