Browsing by Author "Szablikowski, Blazej M."

Now showing 1 - 2 of 2

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.