Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities
This work investigates the quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion–reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dy...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2024-0115 |
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| author | Ahmed Nauman Macías-Díaz Jorge E. Ali Makhdoom Jawaz Muhammad Baber Muhammad Z. Medina-Guevara María G. |
| author_facet | Ahmed Nauman Macías-Díaz Jorge E. Ali Makhdoom Jawaz Muhammad Baber Muhammad Z. Medina-Guevara María G. |
| author_sort | Ahmed Nauman |
| collection | DOAJ |
| description | This work investigates the quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion–reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dynamics of the species. The new extended direct algebraic method is applied to obtain abundant families of solitary wave solutions. Different types of solitary wave solutions are obtained by applying this analytical method. This approach provides the solutions in the form of single and combined wave structures, which are observed in shock, complex solitary-shock, shock-singular, and periodic-singular forms. Some of the solutions are depicted graphically to illustrate the fact that they are, indeed, wave solutions of the mathematical model. |
| format | Article |
| id | doaj-art-e06999d3874c411bbf2a8a2d7c630724 |
| institution | OA Journals |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-e06999d3874c411bbf2a8a2d7c6307242025-08-20T02:13:01ZengDe GruyterOpen Physics2391-54712025-02-012316295910.1515/phys-2024-0115Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearitiesAhmed Nauman0Macías-Díaz Jorge E.1Ali Makhdoom2Jawaz Muhammad3Baber Muhammad Z.4Medina-Guevara María G.5Department of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Tallinn, EstoniaDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Exact Sciences and Technology, Los Lagos University Center, University of Guadalajara, Jalisco, MexicoThis work investigates the quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux terms, which are investigated analytically. Diffusion–reaction equations have a wide range of applications in several scientific areas, such as chemistry, biology, and population dynamics of the species. The new extended direct algebraic method is applied to obtain abundant families of solitary wave solutions. Different types of solitary wave solutions are obtained by applying this analytical method. This approach provides the solutions in the form of single and combined wave structures, which are observed in shock, complex solitary-shock, shock-singular, and periodic-singular forms. Some of the solutions are depicted graphically to illustrate the fact that they are, indeed, wave solutions of the mathematical model.https://doi.org/10.1515/phys-2024-0115extended direct algebraic methodquadratic and quartic nonlinearitiessoliton solutionstraveling-wave solutions |
| spellingShingle | Ahmed Nauman Macías-Díaz Jorge E. Ali Makhdoom Jawaz Muhammad Baber Muhammad Z. Medina-Guevara María G. Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities Open Physics extended direct algebraic method quadratic and quartic nonlinearities soliton solutions traveling-wave solutions |
| title | Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities |
| title_full | Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities |
| title_fullStr | Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities |
| title_full_unstemmed | Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities |
| title_short | Dynamical wave structures for some diffusion--reaction equations with quadratic and quartic nonlinearities |
| title_sort | dynamical wave structures for some diffusion reaction equations with quadratic and quartic nonlinearities |
| topic | extended direct algebraic method quadratic and quartic nonlinearities soliton solutions traveling-wave solutions |
| url | https://doi.org/10.1515/phys-2024-0115 |
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