Wave solutions of the DMBBM equation and the cKG equation using the simple equation method
In this article, we transform the (1 + 1)-dimensional non-linear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the (2 + 1)-dimensional cubic Klein Gordon (cKG) equation, which are the non-linear partial differential equations, into the non-linear ordinary differential equations by us...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-08-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.952668/full |
| _version_ | 1811283610248937472 |
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| author | Jiraporn Sanjun Aungkanaporn Chankaew |
| author_facet | Jiraporn Sanjun Aungkanaporn Chankaew |
| author_sort | Jiraporn Sanjun |
| collection | DOAJ |
| description | In this article, we transform the (1 + 1)-dimensional non-linear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the (2 + 1)-dimensional cubic Klein Gordon (cKG) equation, which are the non-linear partial differential equations, into the non-linear ordinary differential equations by using the traveling wave transformation and solve these solutions with the simple equation method (SEM) with the Bernoulli equation. Two classes of exact explicit solutions-hyperbolic and trigonometric solutions of the associated NLEEs are characterized with some free parameters; we obtain the kink waves and periodic waves. |
| first_indexed | 2024-04-13T02:14:44Z |
| format | Article |
| id | doaj.art-3aa6e52f941e48d190fa53e27fb3cc17 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-13T02:14:44Z |
| publishDate | 2022-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-3aa6e52f941e48d190fa53e27fb3cc172022-12-22T03:07:11ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-08-01810.3389/fams.2022.952668952668Wave solutions of the DMBBM equation and the cKG equation using the simple equation methodJiraporn Sanjun0Aungkanaporn Chankaew1Department of Mathematics, Faculty of Science and Technology, Suratthani Rajabhat University, Suratthani, ThailandEducation Program in Mathematics, Faculty of Education, Suratthani Rajabhat University, Suratthani, ThailandIn this article, we transform the (1 + 1)-dimensional non-linear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the (2 + 1)-dimensional cubic Klein Gordon (cKG) equation, which are the non-linear partial differential equations, into the non-linear ordinary differential equations by using the traveling wave transformation and solve these solutions with the simple equation method (SEM) with the Bernoulli equation. Two classes of exact explicit solutions-hyperbolic and trigonometric solutions of the associated NLEEs are characterized with some free parameters; we obtain the kink waves and periodic waves.https://www.frontiersin.org/articles/10.3389/fams.2022.952668/fulltraveling wave solutionsimple equation methodnon-linear evolution equationsdispersive modified Benjamin-Bona-Mahony equationcubic Klein Gordon equation |
| spellingShingle | Jiraporn Sanjun Aungkanaporn Chankaew Wave solutions of the DMBBM equation and the cKG equation using the simple equation method Frontiers in Applied Mathematics and Statistics traveling wave solution simple equation method non-linear evolution equations dispersive modified Benjamin-Bona-Mahony equation cubic Klein Gordon equation |
| title | Wave solutions of the DMBBM equation and the cKG equation using the simple equation method |
| title_full | Wave solutions of the DMBBM equation and the cKG equation using the simple equation method |
| title_fullStr | Wave solutions of the DMBBM equation and the cKG equation using the simple equation method |
| title_full_unstemmed | Wave solutions of the DMBBM equation and the cKG equation using the simple equation method |
| title_short | Wave solutions of the DMBBM equation and the cKG equation using the simple equation method |
| title_sort | wave solutions of the dmbbm equation and the ckg equation using the simple equation method |
| topic | traveling wave solution simple equation method non-linear evolution equations dispersive modified Benjamin-Bona-Mahony equation cubic Klein Gordon equation |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.952668/full |
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