Invariant Manifolds of Homoclinic Orbits and the Dynamical Consequences of a Super-Homoclinic: a Case Study in R4 With Z2-Symmetry and Integral of Motion
| dc.contributor.author | Bakrani, Sajjad | |
| dc.contributor.author | Lamb, Jeroen S. W. | |
| dc.contributor.author | Turaev, Dmitry | |
| dc.date.accessioned | 2023-10-19T15:11:32Z | |
| dc.date.available | 2023-10-19T15:11:32Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We consider a Z(2)-equivariant flow in R-4 with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit Gamma. We provide criteria for the existence of stable and unstable invariant manifolds of Gamma. We prove that if these manifolds intersect transversely, creating a so-called super-homoclinic, then in any neighborhood of this super-homoclinic there exist infinitely many multi-pulse homoclinic loops. An application to a system of coupled nonlinear Schrodinger equations is considered. (C) 2022 The Authors. Published by Elsevier Inc. | en_US |
| dc.description.sponsorship | Acknowledgments. SB was supported by EU Marie Sklodowska-Curie ITN Critical Transitions in Complex Systems (H2020-MSCA-ITN-2014 643073 CRITICS), European Union ERC Advanced Grant of Sebastian Van Strien (339523 RGDD), and TUBITAK grant (No. 118C236). JSWL thanks the London Mathematical Laboratory, for support through its fellowship programme. DT was supported by Leverhulme Trust (RPG-2021-072), by the grants 19-11-00280 and 19-71-10048 of the Russian Science Foundation (RSF), by the Mathematical Center at the Lobachevsky University of Nizhny Novgorod, and by the grant 075-15-2019-1931 of Russian Ministry of Science and Higher Education. | |
| dc.description.sponsorship | EU Marie Sklodowska-Curie, (H2020-MSCA-ITN-2014 643073); European Union ERC, (339523 RGDD); Lobachevsky University of Nizhny Novgorod, (075-15-2019-1931); London Mathematical Laboratory; Russian Ministry of Science and Higher Education; TUBITAK, (118C236); Leverhulme Trust, (19-11-00280, 19-71-10048, RPG-2021-072); Russian Science Foundation, RSF | |
| dc.description.sponsorship | Engineering and Physical Sciences Research Council [EP/P026001/1] Funding Source: researchfish; EPSRC [EP/P026001/1] Funding Source: UKRI | |
| dc.identifier.doi | 10.1016/j.jde.2022.04.002 | en_US |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.issn | 1090-2732 | |
| dc.identifier.scopus | 2-s2.0-85129075632 | en_US |
| dc.identifier.uri | https://doi.org/10.1016/j.jde.2022.04.002 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12469/5060 | |
| dc.language.iso | en | en_US |
| dc.publisher | Academic Press Inc Elsevier Science | en_US |
| dc.relation.ispartof | Journal of Differential Equations | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Systems | En_Us |
| dc.subject | Classification | En_Us |
| dc.subject | Saddle | En_Us |
| dc.subject | Homoclinic | en_US |
| dc.subject | Systems | |
| dc.subject | Super-homoclinic | en_US |
| dc.subject | Classification | |
| dc.subject | Invariant manifold | en_US |
| dc.subject | Saddle | |
| dc.subject | Coupled Schrodinger equations | en_US |
| dc.title | Invariant Manifolds of Homoclinic Orbits and the Dynamical Consequences of a Super-Homoclinic: a Case Study in R4 With Z2-Symmetry and Integral of Motion | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.id | Bakrani, Sajjad/0000-0001-7814-0992 | |
| gdc.author.scopusid | 57219787223 | |
| gdc.author.scopusid | 7201524636 | |
| gdc.author.scopusid | 7003808185 | |
| gdc.author.wosid | Lamb, Jeroen/D-4310-2015 | |
| gdc.bip.impulseclass | C5 | |
| gdc.bip.influenceclass | C5 | |
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| gdc.coar.access | open access | |
| gdc.coar.type | text::journal::journal article | |
| gdc.collaboration.industrial | false | |
| gdc.description.department | Kadir Has University | |
| gdc.description.departmenttemp | [Bakrani, Sajjad; Lamb, Jeroen S. W.; Turaev, Dmitry] Imperial Coll London, Dept Math, London SW7 2AZ, England; [Bakrani, Sajjad] Kadir Has Univ, Fac Engn & Nat Sci, TR-34083 Istanbul, Turkey | en_US |
| gdc.description.endpage | 63 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q1 | |
| gdc.description.startpage | 1 | en_US |
| gdc.description.volume | 327 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
| gdc.description.wosquality | Q1 | |
| gdc.identifier.openalex | W4225010438 | |
| gdc.identifier.wos | WOS:000819929700001 | en_US |
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