PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws
Version 1
: Received: 12 September 2024 / Approved: 12 September 2024 / Online: 12 September 2024 (13:03:41 CEST)
How to cite:
Kakuli, M. C. Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws. Preprints2024, 2024090989. https://doi.org/10.20944/preprints202409.0989.v1
Kakuli, M. C. Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws. Preprints 2024, 2024090989. https://doi.org/10.20944/preprints202409.0989.v1
Kakuli, M. C. Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws. Preprints2024, 2024090989. https://doi.org/10.20944/preprints202409.0989.v1
APA Style
Kakuli, M. C. (2024). Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws. Preprints. https://doi.org/10.20944/preprints202409.0989.v1
Chicago/Turabian Style
Kakuli, M. C. 2024 "Application of the Generalized Double Reduction Method to the (1+1)-Dimensional Kaup-Boussinesq (K-B) System: Exploiting Lie Symmetries and Conservation Laws" Preprints. https://doi.org/10.20944/preprints202409.0989.v1
Abstract
This paper explores the application of the generalized double reduction method to the (1+1)-dimensional Kaup-Boussinesq (K-B) system, which models nonlinear wave propagation. Double reduction method is a structured and systematic approach in the analysis of partial differential equations (PDEs). We first identify the Lie point symmetries of the K-B 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 B-K system into second-order differential equations or algebraic equations. The reduction process allowed us to derive two exact solutions for the K-B 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 nonlinear systems of PDEs, contributing to a deeper understanding of the systems.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
