Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions
This paper is concerned with the traveling wave solutions and analytical treatment of the simplified MCH equation and the combined KdV–mKdV equations. Based on a polynomial about x and t, the rational solutions are investigated. The abundant soliton and periodic wave solutions are obtained by using...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123001122 |
| _version_ | 1797260320842973184 |
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| author | Nawzad Hasan Ali Sizar Abid Mohammed Jalil Manafian |
| author_facet | Nawzad Hasan Ali Sizar Abid Mohammed Jalil Manafian |
| author_sort | Nawzad Hasan Ali |
| collection | DOAJ |
| description | This paper is concerned with the traveling wave solutions and analytical treatment of the simplified MCH equation and the combined KdV–mKdV equations. Based on a polynomial about x and t, the rational solutions are investigated. The abundant soliton and periodic wave solutions are obtained by using a direct function. The hyperbolic-type and trigonometric-type solutions are given by utilizing the improved tan(ϕ/2)-expansion method. The dynamic properties of these derived results are shown in some three-dimensional, density and 2D plots. Traveling wave solutions are utilized to depict water waves in the mentioned equations, and that is used in physical science to model quantum field theory, dust-acoustic waves, ion acoustic waves, which is taken into account through the application of the improved tan(ϕ/2)-expansion technique. In addition, the recommended technique allowed us to produce some dynamical wave patterns of kink, kink single soliton, single soliton, compacton, periodic shape and other structures are developed, which are shown using three-dimensional, density and 2D plots to more clearly illustrate the physical layout. The method is one of the proficient and effective approaches which have swiftly developed in order to searching appropriate responses to partial differential equations with nonlinear sciences. |
| first_indexed | 2024-03-08T23:37:23Z |
| format | Article |
| id | doaj.art-0eb5d180a14c4c448f103ae8332a18ce |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T23:23:27Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-0eb5d180a14c4c448f103ae8332a18ce2024-03-16T05:09:26ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-03-019100599Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutionsNawzad Hasan Ali0Sizar Abid Mohammed1Jalil Manafian2Department of Medical Education, College of Medicine, University of Duhok, IraqDepartment of Mathematics, College of Basic Education, University of Duhok, Zakho, IraqDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan; Corresponding author at: Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.This paper is concerned with the traveling wave solutions and analytical treatment of the simplified MCH equation and the combined KdV–mKdV equations. Based on a polynomial about x and t, the rational solutions are investigated. The abundant soliton and periodic wave solutions are obtained by using a direct function. The hyperbolic-type and trigonometric-type solutions are given by utilizing the improved tan(ϕ/2)-expansion method. The dynamic properties of these derived results are shown in some three-dimensional, density and 2D plots. Traveling wave solutions are utilized to depict water waves in the mentioned equations, and that is used in physical science to model quantum field theory, dust-acoustic waves, ion acoustic waves, which is taken into account through the application of the improved tan(ϕ/2)-expansion technique. In addition, the recommended technique allowed us to produce some dynamical wave patterns of kink, kink single soliton, single soliton, compacton, periodic shape and other structures are developed, which are shown using three-dimensional, density and 2D plots to more clearly illustrate the physical layout. The method is one of the proficient and effective approaches which have swiftly developed in order to searching appropriate responses to partial differential equations with nonlinear sciences.http://www.sciencedirect.com/science/article/pii/S2666818123001122Improved tan(ϕ/2)-expansion techniqueKink single solitonSingle solitonCompactonTraveling wave solutions equations |
| spellingShingle | Nawzad Hasan Ali Sizar Abid Mohammed Jalil Manafian Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions Partial Differential Equations in Applied Mathematics Improved tan(ϕ/2)-expansion technique Kink single soliton Single soliton Compacton Traveling wave solutions equations |
| title | Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions |
| title_full | Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions |
| title_fullStr | Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions |
| title_full_unstemmed | Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions |
| title_short | Study on the simplified MCH equation and the combined KdV–mKdV equations with solitary wave solutions |
| title_sort | study on the simplified mch equation and the combined kdv mkdv equations with solitary wave solutions |
| topic | Improved tan(ϕ/2)-expansion technique Kink single soliton Single soliton Compacton Traveling wave solutions equations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123001122 |
| work_keys_str_mv | AT nawzadhasanali studyonthesimplifiedmchequationandthecombinedkdvmkdvequationswithsolitarywavesolutions AT sizarabidmohammed studyonthesimplifiedmchequationandthecombinedkdvmkdvequationswithsolitarywavesolutions AT jalilmanafian studyonthesimplifiedmchequationandthecombinedkdvmkdvequationswithsolitarywavesolutions |