3 papers
nlin.SI2025
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…
nlin.SI2025
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…
nlin.SI2025
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…