مشروع البحث: On finding exact solutions of some nonlinear partial differential equations based on Riccati oquation
| dc.contributor.advisor | د. ابراهيم محمد حسن | |
| dc.date.accessioned | 2025-03-11T11:15:19Z | |
| dc.date.available | 2025-03-11T11:15:19Z | |
| dc.description | This thesis deals with problems arising in the study of nonlinear partial differential equations (PDEs). Three methods have applied for constructing the exact traveling wave solutions of some nonlinear PDEs with the aid of the generalized Riccati equation 2 '( ) r p ( ) q ( ) and Maple software. This thesis contains three chapters. In chapter one, we apply the generalized Riccati equation mapping method to find the exact traveling wave solutions of the generalized nonlinear Gardner equation and the generalized KdV-mKdV equation with higher-order nonlinear terms. In chapter two, we apply the Bäcklund transformation of the Riccati equation to find the exact traveling wave solutions of the generalized KdV-mKdV equation with higher-order nonlinear terms and the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. In chapter three, we apply the (G′/G)-expansion method to find the exact traveling wave solutions of the nonlinear PDE describing the nonlinear low-pass electrical lines and the nonlinear modified KdV equation. Finally, comparison between our recent results and the well-known results is given. We end this abstract with the remark that, we have published two papers from this thesis, see [19]. | |
| dc.description.abstract | This thesis deals with problems arising in the study of nonlinear partial differential equations (PDEs). Three methods have applied for constructing the exact traveling wave solutions of some nonlinear PDEs with the aid of the generalized Riccati equation 2 '( ) r p ( ) q ( ) and Maple software. This thesis contains three chapters. In chapter one, we apply the generalized Riccati equation mapping method to find the exact traveling wave solutions of the generalized nonlinear Gardner equation and the generalized KdV-mKdV equation with higher-order nonlinear terms. In chapter two, we apply the Bäcklund transformation of the Riccati equation to find the exact traveling wave solutions of the generalized KdV-mKdV equation with higher-order nonlinear terms and the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. In chapter three, we apply the (G′/G)-expansion method to find the exact traveling wave solutions of the nonlinear PDE describing the nonlinear low-pass electrical lines and the nonlinear modified KdV equation. Finally, comparison between our recent results and the well-known results is given. We end this abstract with the remark that, we have published two papers from this thesis, see [19]. | |
| dc.identifier | 7001 | |
| dc.identifier.uri | https://dspace.academy.edu.ly/handle/123456789/1465 | |
| dc.subject | On finding exact solutions of some nonlinear partial differential equations based on Riccati oquation | |
| dc.title | On finding exact solutions of some nonlinear partial differential equations based on Riccati oquation | |
| dspace.entity.type | Project | |
| project.endDate | 2019 | |
| project.funder.name | رياضيات | |
| project.investigator | محمد عمر المريض | |
| project.startDate | 2018 | |
| relation.isOrgUnitOfProject | abd0d318-9280-4b6c-a480-6db4a3a7c674 | |
| relation.isOrgUnitOfProject.latestForDiscovery | abd0d318-9280-4b6c-a480-6db4a3a7c674 |