Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws
This paper explores the application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq system, which models nonlinear wave propagation. Generalized double reduction method is a structured and systematic approach in the analysis of partial differential equations. We f...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003905 |
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| author | Molahlehi Charles Kakuli |
| author_facet | Molahlehi Charles Kakuli |
| author_sort | Molahlehi Charles Kakuli |
| collection | DOAJ |
| description | This paper explores the application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq system, which models nonlinear wave propagation. Generalized double reduction method is a structured and systematic approach in the analysis of partial differential equations. We first identify the Lie point symmetries of the Kaup–Boussinesq system and construct four non-trivial conservation laws using the multiplier method. The association between the Lie point symmetries and the conservation laws is established, and the generalized double reduction method is then applied to transform the Kaup–Boussinesq system into second-order differential equations or algebraic equations. The reduction process allowed us to derive two exact solutions for the Kaup–Boussinesq system, illustrating the method’s effectiveness in handling nonlinear systems. This work highlights the effectiveness of the generalized double reduction method in simplifying and solving nonlinear systems of partial differential equations, contributing to a deeper understanding of the systems. |
| format | Article |
| id | doaj-art-8b36208c6bd045e88b5d7a38373aba12 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-8b36208c6bd045e88b5d7a38373aba122024-12-13T11:05:56ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112101004Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation lawsMolahlehi Charles Kakuli0Department of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, Republic of South AfricaThis paper explores the application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq system, which models nonlinear wave propagation. Generalized double reduction method is a structured and systematic approach in the analysis of partial differential equations. We first identify the Lie point symmetries of the Kaup–Boussinesq system and construct four non-trivial conservation laws using the multiplier method. The association between the Lie point symmetries and the conservation laws is established, and the generalized double reduction method is then applied to transform the Kaup–Boussinesq system into second-order differential equations or algebraic equations. The reduction process allowed us to derive two exact solutions for the Kaup–Boussinesq system, illustrating the method’s effectiveness in handling nonlinear systems. This work highlights the effectiveness of the generalized double reduction method in simplifying and solving nonlinear systems of partial differential equations, contributing to a deeper understanding of the systems.http://www.sciencedirect.com/science/article/pii/S2666818124003905Generalized double reduction methodConservation lawsKaup-Boussinesq systemLie symmetry analysisExact solutions |
| spellingShingle | Molahlehi Charles Kakuli Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws Partial Differential Equations in Applied Mathematics Generalized double reduction method Conservation laws Kaup-Boussinesq system Lie symmetry analysis Exact solutions |
| title | Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws |
| title_full | Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws |
| title_fullStr | Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws |
| title_full_unstemmed | Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws |
| title_short | Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws |
| title_sort | application of the generalized double reduction method to the 1 1 dimensional kaup boussinesq k b system exploiting lie symmetries and conservation laws |
| topic | Generalized double reduction method Conservation laws Kaup-Boussinesq system Lie symmetry analysis Exact solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003905 |
| work_keys_str_mv | AT molahlehicharleskakuli applicationofthegeneralizeddoublereductionmethodtothe11dimensionalkaupboussinesqkbsystemexploitingliesymmetriesandconservationlaws |