127 citations · 969 across the 51 of their papers we have counts for
51 papers
Bäcklund transformations as integrable discretization. The geometric approach
Adam Doliwa
We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the "discretization by Bäcklund transformations" point of view. We…
Non-autonomous multidimensional Toda system and multiple interpolation problem
Adam Doliwa
We study the interpolation analogue of the Hermite-Padé type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete sy…
Non-commutative Hermite--Padé approximation and integrability
Adam Doliwa
We introduce and solve the non-commutative version of the Hermite-Padé type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subcl…
Hermite-Padé approximation and integrability
Adam Doliwa, Artur Siemaszko
We show that solution to the Hermite-Padé type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev-Petviashvili) system and…
Integrability and geometry of the Wynn recurrence
Adam Doliwa, Artur Siemaszko
We show that the Wynn recurrence (the missing identity of Frobenius of the Padé approximation theory) can be incorporated into the theory of integrable systems as a reduction of th…
Discrete Darboux system with self-consistent sources and its symmetric reduction
Adam Doliwa, Runliang Lin, Zhe Wang
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and t…