Bi-Hamiltonian Structures for Integrable Systems on Regular Time Scales
| dc.contributor.author | Szablikowski, Blazej M. | |
| dc.contributor.author | Blaszak, Maciej | |
| dc.contributor.author | Silindir, Burcu | |
| dc.date.accessioned | 2023-06-16T14:18:43Z | |
| dc.date.available | 2023-06-16T14:18:43Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | 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. | en_US |
| dc.description.sponsorship | Scientific and Technical Research Council of Turkey; MNiSW research Grant [N NN202 404933]; European Community [PIEF-GA-2008-221624] | en_US |
| dc.description.sponsorship | This work was partially supported by the Scientific and Technical Research Council of Turkey and MNiSW research Grant No. N NN202 404933. B. S. was supported by the European Community under a Marie Curie Intra-European Fellowship, Contract No. PIEF-GA-2008-221624. | en_US |
| dc.identifier.doi | 10.1063/1.3158860 | |
| dc.identifier.issn | 0022-2488 | |
| dc.identifier.issn | 1089-7658 | |
| dc.identifier.scopus | 2-s2.0-68749108374 | |
| dc.identifier.uri | https://doi.org/10.1063/1.3158860 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14365/1549 | |
| dc.language.iso | en | en_US |
| dc.publisher | Amer Inst Physics | en_US |
| dc.relation.ispartof | Journal of Mathematıcal Physıcs | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | functional analysis | en_US |
| dc.subject | Poisson equation | en_US |
| dc.subject | recursive functions | en_US |
| dc.subject | tensors | en_US |
| dc.subject | Operators | en_US |
| dc.subject | Algebra | en_US |
| dc.title | Bi-Hamiltonian Structures for Integrable Systems on Regular Time Scales | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.id | Szablikowski, Blazej/0000-0002-4001-6328 | |
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| gdc.description.department | İzmir Ekonomi Üniversitesi | en_US |
| gdc.description.departmenttemp | [Szablikowski, Blazej M.] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland; [Szablikowski, Blazej M.; Blaszak, Maciej] Adam Mickiewicz Univ Poznan, Dept Phys, PL-61614 Poznan, Poland; [Silindir, Burcu] Izmir Univ Econ, Dept Math, TR-35330 Izmir, Turkey | en_US |
| gdc.description.issue | 7 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q3 | |
| gdc.description.volume | 50 | en_US |
| gdc.description.wosquality | Q3 | |
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| gdc.oaire.keywords | Nonlinear Sciences - Exactly Solvable and Integrable Systems | |
| gdc.oaire.keywords | FOS: Physical sciences | |
| gdc.oaire.keywords | Exactly Solvable and Integrable Systems (nlin.SI) | |
| gdc.oaire.keywords | Dynamic equations on time scales or measure chains | |
| gdc.oaire.keywords | recursive functions | |
| gdc.oaire.keywords | tensors | |
| gdc.oaire.keywords | Partial functional-differential equations | |
| gdc.oaire.keywords | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) | |
| gdc.oaire.keywords | Lattice dynamics; integrable lattice equations | |
| gdc.oaire.keywords | Poisson equation | |
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| gdc.virtual.author | Yantır Silindir, Burcu | |
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