70 citations · 296 across the 22 of their papers we have counts for
22 papers
From pencils of Novikov algebras of Stäckel type to soliton hierarchies
Maciej Błaszak, Krzysztof Marciniak, Błażej M. Szablikowski
In this article we construct evolutionary soliton hierarchies from pencils of Novikov algebras of Stäckel type. We start by defining a special class of associative Novikov algebras…
Stationary systems of the AKNS hierarchy
Maciej Błaszak, Krzysztof Marciniak, Błażej M. Szablikowski
In this article we investigate stationary systems of the AKNS hierarchy. We prove that all these systems are classical separable Stäckel systems. The explicit transformation from j…
Non-autonomous soliton hierarchies
Maciej Błaszak, Krzysztof Marciniak, Błażej M. Szablikowski
A formalism of systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for…
Stationary coupled KdV systems and their Stäckel representations
Błażej M. Szablikowski, Maciej Błaszak, Krzysztof Marciniak
In this article we investigate stationary cKdV systems and prove that every -field stationary cKdV system can be written, after a careful reparametrization of jet variables, as…
Stäckel representations of stationary KdV systems
Maciej Błaszak, Błażej M. Szablikowski, Krzysztof Marciniak
In this article we study Stäckel representations of stationary KdV systems. Using Lax formalism we prove that these systems have two different representations as separable Stäckel…
Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras
Błażej M. Szablikowski
The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introduci…
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
Blazej M. Szablikowski
The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear ope…
Integrable quantum Stäckel systems
Maciej Blaszak, Ziemowit Domanski, Artur Sergyeyev +1
The Stäckel separability of a Hamiltonian system is well known to ensure existence of a complete set of Poisson commuting integrals of motion quadratic in the momenta. In the prese…
Classical -matrix like approach to Frobenius manifolds, WDVV equations and flat metrics
Blazej M. Szablikowski
A general scheme for construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to WDVV associativity equations is formulated. The a…
Construction and separability of nonlinear soliton integrable couplings
Maciej Blaszak, Blazej M. Szablikowski, Burcu Silindir
A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of…
Classical R-matrix theory for bi-Hamiltonian field systems
Maciej Blaszak, Blazej M. Szablikowski
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras…
Bi-Hamiltonian structures for integrable systems on regular time scales
Blazej M. Szablikowski, Maciej Blaszak, Burcu Silindir
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of -pseudo-differential operators,…
Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
Artur Sergyeyev, Blazej M. Szablikowski
We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/031…
R-matrix approach to integrable systems on time scales
Maciej Blaszak, Burcu Silindir, Blazej M. Szablikowski
A general unifying framework for integrable soliton-like systems on time scales is introduced. The -matrix formalism is applied to the algebra of -differential operators in t…
Integrable discrete systems on R and related dispersionless systems
Maciej Blaszak, Metin Gurses, Burcu Silindir +1
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grai…
Dispersionful analogue of the Whitham hierarchy
Blazej M. Szablikowski, Maciej Blaszak
The dispersionful analogue, by means of Lax formalism, of the zero-genus universal Whitham hierarchy together with its algebraic orbit finite-field reductions is considered. The th…
Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems
Blazej M. Szablikowski, Maciej Blaszak
Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented.…
Gauge transformation and reciprocal link for (2+1)-dimensional integrable field systems
Blazej M. Szablikowski
Appropriate restrictions of Lax operators which allows to construction of (2+1)-dimensional integrable field systems, coming from centrally extended algebra of pseudo-differential…
On deformations of standard R-matrices for integrable infinite-dimensional systems
Blazej M. Szablikowski, Maciej Blaszak
Simple deformations, with a parameter , of classical -matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax repres…
From dispersionless to soliton systems via Weyl-Moyal like deformations
Maciej Blaszak, Blazej Szablikowski
The formalism of quantization deformation is reviewed and the Weyl-Moyal like deformation is applied to systematic construction of the field and lattice integrable soliton systems…
Classical R-matrix theory of dispersionless systems: II. (2+1)-dimension theory
Maciej Blaszak, Blazej M. Szablikowski
A systematic way of construction of (2+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the so-called central extension procedure a…
Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
Maciej Blaszak, Blazej M. Szablikowski
A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras…