Browsing by Author "Blaszak, Maciej"

Now showing 1 - 3 of 3

Citation - WoS: 5
Citation - Scopus: 5
Bi-Hamiltonian Structures for Integrable Systems on Regular Time Scales
(Amer Inst Physics, 2009) Szablikowski, Blazej M.; Blaszak, Maciej; Silindir, Burcu
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of delta-pseudodifferential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors are given by the use of the recursion operators of the Lax hierarchies. The theory is illustrated by Delta-differential counterparts of Ablowitz-Kaup-Newell-Segur and Kaup-Broer hierarchies.
Citation - WoS: 5
Citation - Scopus: 6
Construction and Separability of Nonlinear Soliton Integrable Couplings
(Elsevier Science Inc, 2012) Blaszak, Maciej; Szablikowski, Blazej M.; Silindir, Burcu
The paper is motivated by recent works of several authors, initiated by articles of Ma and Zhu [W. X. Ma, Z. N. Zhu, Constructing nonlinear discrete integrable Hamiltonian couplings, Comput. Math. Appl. 60 (2010) 2601] and Ma [W. X. Ma, Nonlinear continuous integrable Hamiltonian couplings, Appl. Math. Comput. 217 (2011) 7238], where new class of soliton systems, being nonlinear integrable couplings, was introduced. Here, we present a general construction of such class of systems and we develop the decoupling procedure, separating them into copies of underlying original equations. (C) 2012 Elsevier Inc. All rights reserved.
Flat Minimal Quantizations of Stackel Systems and Quantum Separability
(Academic Press Inc Elsevier Science, 2014) Blaszak, Maciej; Domanski, Ziemowit; Silindir, Burcu
In this paper, we consider the problem of quantization of classical Stackel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stackel transform, natural Hamiltonian systems from a given Riemann space are expressed by some flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stackel systems which remains separable after any of admissible flat minimal quantizations. (C) 2014 Elsevier Inc. All rights reserved.