28 citations · 51 across the 8 of their papers we have counts for
8 papers
NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks
Oleksandr Chvartatskyi, Folkert Müller-Hoissen
The infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (NLS) equation are obtained via a matrix version of the Dar…
Generalized Volterra lattices: binary Darboux transformations and self-consistent sources
Folkert Müller-Hoissen, Oleksandr Chvartatskyi, Kouichi Toda
We study two families of (matrix versions of) generalized Volterra (or Bogoyavlensky) lattice equations. For each family, the equations arise as reductions of a partial differentia…
Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations
Oleksandr Chvartatskyi, Aristophanes Dimakis, Folkert Müller-Hoissen
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation…
Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy
Oleksandr Chvartatskyi, Yuriy Sydorenko
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of -dimensional integrable equations,…
'Riemann Equations' in Bidifferential Calculus
Oleksandr Chvartatskyi, Folkert Mueller-Hoissen, Nikola Stoilov
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential…
A new (1+1)-dimensional matrix k-constrained KP hierarchy
Oleksandr Chvartatskyi, Yuriy Sydorenko
We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensio…
A new bidirectional generalization of (2+1)-dimensional matrix k-constrained KP hierarchy
Oleksandr Chvartatskyi, Yuriy Sydorenko
We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained KP hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy,…
Matrix generalizations of integrable systems with Lax integro-differential representations
Oleksandr Chvartatskyi, Yuriy Sydorenko
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-…