Analyzing invariants and employing successive reductions for the extended Kadomtsev Petviashvili equation in (3+1) dimensions
In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to...
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| Published in | PloS one Vol. 19; no. 7; p. e0305177 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Public Library of Science
02.07.2024
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| Abstract | In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to the derivation of an optimal system of one-dimensional subalgebras relevant to the equation. This optimal system is utilized to obtain several invariant solutions. The Lie group method is subsequently applied to the reduced governing equations derived from the given equation. We complement our findings with Mathematica simulations illustrating some of the obtained solutions. Furthermore, a direct approach is used to investigate local conservation laws. Importantly, our study addresses a gap in the exploration of the 3D-EXP equation using group theoretic methods, making our findings novel in this context. |
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| AbstractList | In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to the derivation of an optimal system of one-dimensional subalgebras relevant to the equation. This optimal system is utilized to obtain several invariant solutions. The Lie group method is subsequently applied to the reduced governing equations derived from the given equation. We complement our findings with Mathematica simulations illustrating some of the obtained solutions. Furthermore, a direct approach is used to investigate local conservation laws. Importantly, our study addresses a gap in the exploration of the 3D-EXP equation using group theoretic methods, making our findings novel in this context. In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to the derivation of an optimal system of one-dimensional subalgebras relevant to the equation. This optimal system is utilized to obtain several invariant solutions. The Lie group method is subsequently applied to the reduced governing equations derived from the given equation. We complement our findings with Mathematica simulations illustrating some of the obtained solutions. Furthermore, a direct approach is used to investigate local conservation laws. Importantly, our study addresses a gap in the exploration of the 3D-EXP equation using group theoretic methods, making our findings novel in this context.In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of Lie point symmetries associated with the equation, leading to the derivation of an optimal system of one-dimensional subalgebras relevant to the equation. This optimal system is utilized to obtain several invariant solutions. The Lie group method is subsequently applied to the reduced governing equations derived from the given equation. We complement our findings with Mathematica simulations illustrating some of the obtained solutions. Furthermore, a direct approach is used to investigate local conservation laws. Importantly, our study addresses a gap in the exploration of the 3D-EXP equation using group theoretic methods, making our findings novel in this context. |
| Audience | Academic |
| Author | Sallah, Mohammed Hussain, Akhtar Owyed, Saud Zaman, F D Herrera, Jorge |
| AuthorAffiliation | 1 Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan College of Mathematics and Systems Science, Shandong University of Science and Technology, CHINA 4 Applied Mathematical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt 3 Facultad de Ciencias Naturales e Ingenieria, Universidad de Bogota Jorge Tadeo Lozano, Bogota, Colombia 2 Mathematics Department, College of Science, University of Bisha, Bisha, Saudi Arabia |
| AuthorAffiliation_xml | – name: 2 Mathematics Department, College of Science, University of Bisha, Bisha, Saudi Arabia – name: 4 Applied Mathematical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt – name: 1 Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan – name: 3 Facultad de Ciencias Naturales e Ingenieria, Universidad de Bogota Jorge Tadeo Lozano, Bogota, Colombia – name: College of Mathematics and Systems Science, Shandong University of Science and Technology, CHINA |
| Author_xml | – sequence: 1 givenname: Akhtar orcidid: 0000-0002-1892-3212 surname: Hussain fullname: Hussain, Akhtar organization: Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan – sequence: 2 givenname: F D orcidid: 0000-0002-6498-0664 surname: Zaman fullname: Zaman, F D organization: Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan – sequence: 3 givenname: Saud surname: Owyed fullname: Owyed, Saud organization: Mathematics Department, College of Science, University of Bisha, Bisha, Saudi Arabia – sequence: 4 givenname: Jorge surname: Herrera fullname: Herrera, Jorge organization: Facultad de Ciencias Naturales e Ingenieria, Universidad de Bogota Jorge Tadeo Lozano, Bogota, Colombia – sequence: 5 givenname: Mohammed orcidid: 0000-0003-2063-8979 surname: Sallah fullname: Sallah, Mohammed organization: Applied Mathematical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt |
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| Copyright | Copyright: © 2024 Hussain et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. COPYRIGHT 2024 Public Library of Science 2024 Hussain et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2024 Hussain et al 2024 Hussain et al |
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| Snippet | In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP)... |
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| SubjectTerms | Algebra Algorithms Computer and Information Sciences Computer Simulation Conservation laws Earth Sciences Environmental law Exact solutions Invariants Investigations Lie groups Mathematics Models, Theoretical Partial differential equations Physical Sciences Physics Symmetry |
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| Title | Analyzing invariants and employing successive reductions for the extended Kadomtsev Petviashvili equation in (3+1) dimensions |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/38954677 https://www.proquest.com/docview/3075014270/abstract/ https://www.proquest.com/docview/3075373116/abstract/ https://pubmed.ncbi.nlm.nih.gov/PMC11218999 |
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