Integrability via Functional Expansion for the KMN Model
This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a q...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1819 |
| _version_ | 1797548932294770688 |
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| author | Radu Constantinescu Aurelia Florian |
| author_facet | Radu Constantinescu Aurelia Florian |
| author_sort | Radu Constantinescu |
| collection | DOAJ |
| description | This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included. |
| first_indexed | 2024-03-10T15:07:46Z |
| format | Article |
| id | doaj.art-257355327ada43fea770a31f607e4d75 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T15:07:46Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-257355327ada43fea770a31f607e4d752023-11-20T19:35:34ZengMDPI AGSymmetry2073-89942020-11-011211181910.3390/sym12111819Integrability via Functional Expansion for the KMN ModelRadu Constantinescu0Aurelia Florian1Department of Physics, University of Craiova, A.I.Cuza 13, 200585 Craiova, RomaniaDepartment of Physics, University of Craiova, A.I.Cuza 13, 200585 Craiova, RomaniaThis paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.https://www.mdpi.com/2073-8994/12/11/1819functional expansiontraveling wavesKMN equation |
| spellingShingle | Radu Constantinescu Aurelia Florian Integrability via Functional Expansion for the KMN Model Symmetry functional expansion traveling waves KMN equation |
| title | Integrability via Functional Expansion for the KMN Model |
| title_full | Integrability via Functional Expansion for the KMN Model |
| title_fullStr | Integrability via Functional Expansion for the KMN Model |
| title_full_unstemmed | Integrability via Functional Expansion for the KMN Model |
| title_short | Integrability via Functional Expansion for the KMN Model |
| title_sort | integrability via functional expansion for the kmn model |
| topic | functional expansion traveling waves KMN equation |
| url | https://www.mdpi.com/2073-8994/12/11/1819 |
| work_keys_str_mv | AT raduconstantinescu integrabilityviafunctionalexpansionforthekmnmodel AT aureliaflorian integrabilityviafunctionalexpansionforthekmnmodel |