{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T02:56:14Z","timestamp":1772765774825,"version":"3.50.1"},"reference-count":77,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005992","name":"Ministry of Education and Science","doi-asserted-by":"publisher","award":["D01205\/23.11.2018"],"award-info":[{"award-number":["D01205\/23.11.2018"]}],"id":[{"id":"10.13039\/501100005992","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Republic of Bulgaria","award":["BG05 M2OP0001-1.0001-0008"],"award-info":[{"award-number":["BG05 M2OP0001-1.0001-0008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities. We present an amended version of the methodology, which is based on the use of composite functions. The number of steps of the SEsM was reduced from seven to four in the amended version of the methodology. For the case of nonlinear differential equations with polynomial nonlinearities, SEsM can reduce the solved equations to a system of nonlinear algebraic equations. Each nontrivial solution of this algebraic system leads to an exact solution of the solved nonlinear differential equations. We prove the theorems and present examples for the use of composite functions in the methodology of the SEsM for the following three kinds of composite functions: (i) a composite function of one function of one independent variable; (ii) a composite function of two functions of two independent variables; (iii) a composite function of three functions of two independent variables.<\/jats:p>","DOI":"10.3390\/computation9100104","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T04:55:33Z","timestamp":1632718533000},"page":"104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["On the Use of Composite Functions in the Simple Equations Method to Obtain Exact Solutions of Nonlinear Differential Equations"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6209-547X","authenticated-orcid":false,"given":"Nikolay K.","family":"Vitanov","sequence":"first","affiliation":[{"name":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 4, 1113 Sofia, Bulgaria"}]},{"given":"Zlatinka I.","family":"Dimitrova","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 4, 1113 Sofia, Bulgaria"}]},{"given":"Kaloyan N.","family":"Vitanov","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 4, 1113 Sofia, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Latora, V., Nicosia, V., and Russo, G. (2017). Complex Networks. Principles, Methods, and Applications, Cambridge University Press.","DOI":"10.1017\/9781316216002"},{"key":"ref_2","unstructured":"Chian, A.C.-L. (2007). Complex Systems Approach to Economic Dynamics, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Vitanov, N.K. (2016). Science Dynamics and Research Production. 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