{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T12:51:02Z","timestamp":1775047862909,"version":"3.50.1"},"reference-count":72,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T00:00:00Z","timestamp":1627344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study, we consider a two-field cosmological model with scalar fields defined in the Jordan frame. In particular, we consider a Brans\u2013Dicke scalar field theory and for the second scalar field we consider a quintessence scalar field minimally coupled to gravity. For this cosmological model, we apply for the first time a new technique for the derivation of conservation laws without the application of variational symmetries. The results are applied for the derivation of new exact solutions. The stability properties of the scaling solutions are investigated and criteria for the nature of the second field according to the stability of these solutions are determined.<\/jats:p>","DOI":"10.3390\/sym13081364","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T22:35:02Z","timestamp":1627425302000},"page":"1364","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["New Conservation Laws and Exact Cosmological Solutions in Brans\u2013Dicke Cosmology with an Extra Scalar Field"],"prefix":"10.3390","volume":"13","author":[{"given":"Antonios","family":"Mitsopoulos","sequence":"first","affiliation":[{"name":"Faculty of Physics, Department of Astronomy-Astrophysics-Mechanics, University of Athens, Panepistemiopolis, 15783 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Tsamparlis","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Department of Astronomy-Astrophysics-Mechanics, University of Athens, Panepistemiopolis, 15783 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1152-6548","authenticated-orcid":false,"given":"Genly","family":"Leon","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9966-5517","authenticated-orcid":false,"given":"Andronikos","family":"Paliathanasis","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"},{"name":"Instituto de Ciencias F\u00edsicas y Matem\u00e1ticas, Universidad Austral de Chile, Valdivia 5090000, Regi\u00f3n de Los R\u00edos, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1086\/300499","article-title":"Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant","volume":"116","author":"Riess","year":"1998","journal-title":"Astron. 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