Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission
Graphene has appeared as one of the most promising nanomaterials with unique thermal, electronic and mechanical properties which make it suitable for many applications in materials science, energy storage, electronics, water filtration and medicine. In this paper, we have studied the (2+1)-dimension...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-05-01
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| Series: | Alexandria Engineering Journal |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824002898 |
| _version_ | 1797234030359347200 |
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| author | Mahmoud Gaballah Rehab M. El-Shiekh |
| author_facet | Mahmoud Gaballah Rehab M. El-Shiekh |
| author_sort | Mahmoud Gaballah |
| collection | DOAJ |
| description | Graphene has appeared as one of the most promising nanomaterials with unique thermal, electronic and mechanical properties which make it suitable for many applications in materials science, energy storage, electronics, water filtration and medicine. In this paper, we have studied the (2+1)-dimensional graphene sheets (GS) equation with variable heat transmission thermophoretic motion by using both Bäcklund transformation and similarity reduction techniques. As a result, from Bäcklund transformation one soliton solution was obtained and from similarity reduction technique the GS equation is reduced to a nonlinear ordinary differential equation which can be solved using the trial equation method; where many novel wave solutions were obtained. As an additional remark, the Bäcklund transformation obtained can be found by the traditional Painléve test. Finally, some graphs are given to illustrate the effect of the variable coefficients on the behavior of the thermal wave transmission. |
| first_indexed | 2024-04-24T16:25:35Z |
| format | Article |
| id | doaj.art-3f346adf9dc4411fbf0bba62a899b8ef |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-24T16:25:35Z |
| publishDate | 2024-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-3f346adf9dc4411fbf0bba62a899b8ef2024-03-31T04:37:09ZengElsevierAlexandria Engineering Journal1110-01682024-05-01952429Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmissionMahmoud Gaballah0Rehab M. El-Shiekh1Geomagnetic and Geoelectric Department, National Research Institute of Astronomy and Geophysics (NRIAG), 11421 Helwan, Cairo, Egypt; Department of Physics, College of Science at Al-Zulfi, Majmaah University 11952, Kingdom of Saudi Arabia; Corresponding author.Department of Business Administration, College of Business Administration in Majmaah, Majmaah University 11952, Kingdom of Saudi Arabia; Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptGraphene has appeared as one of the most promising nanomaterials with unique thermal, electronic and mechanical properties which make it suitable for many applications in materials science, energy storage, electronics, water filtration and medicine. In this paper, we have studied the (2+1)-dimensional graphene sheets (GS) equation with variable heat transmission thermophoretic motion by using both Bäcklund transformation and similarity reduction techniques. As a result, from Bäcklund transformation one soliton solution was obtained and from similarity reduction technique the GS equation is reduced to a nonlinear ordinary differential equation which can be solved using the trial equation method; where many novel wave solutions were obtained. As an additional remark, the Bäcklund transformation obtained can be found by the traditional Painléve test. Finally, some graphs are given to illustrate the effect of the variable coefficients on the behavior of the thermal wave transmission.http://www.sciencedirect.com/science/article/pii/S1110016824002898 |
| spellingShingle | Mahmoud Gaballah Rehab M. El-Shiekh Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission Alexandria Engineering Journal |
| title | Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| title_full | Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| title_fullStr | Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| title_full_unstemmed | Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| title_short | Bäcklund transformation, similarity reduction and new solutions for the (2+1)-dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| title_sort | backlund transformation similarity reduction and new solutions for the 2 1 dimensional graphene sheets thermophoretic motion equation with variable heat transmission |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824002898 |
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