6 citations · 9 across the 5 of their papers we have counts for
5 papers
Algebro-geometric integration of the Boussinesq hierarchy
Julia Bernatska, Taras Skrypnyk
We construct an integrable hierarchy of the Boussinesq equation using the Lie-algebraic approach of Holod-Flashka-Newell-Ratiu. We show that finite-gap hamiltonian systems of the h…
Exact quasi-periodic solutions to the MKdV equation
Julia Bernatska
In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop alg…
Exact quasi-periodic solutions to the sine(sinh)-Gordon equations: The method for computation and analysis
Julia Bernatska
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the -functions that uniformize th…
Computation of -functions on plane algebraic curves
Julia Bernatska
Numerical tools for computation of -functions, also known as Kleinian, or multiply periodic, are proposed. In this connection, computation of periods of the both first and sec…
Reality conditions for the KdV equation and exact quasi-periodic solutions in finite phase spaces
Julia Bernatska
In the present paper reality conditions for quasi-periodic solutions of the KdV equation are determined completely. As a result, solutions in the form of non-linear waves can be pl…