Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations
The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoy...
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| Published in | PloS one Vol. 18; no. 3; p. e0283569 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
30.03.2023
Public Library of Science (PLoS) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1932-6203 1932-6203 |
| DOI | 10.1371/journal.pone.0283569 |
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| Abstract | The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions. |
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| AbstractList | The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions.The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions. The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions. |
| Audience | Academic |
| Author | Khan, Adnan Amin, Amina Naeem, Imran |
| AuthorAffiliation | China University of Mining and Technology, CHINA 1 Department of Mathematics, National College of Business Administration & Economics, Lahore Gulberg III, Pakistan 2 Department of Mathematics, Lahore University of Management Sciences, Lahore Cantt., Pakistan |
| AuthorAffiliation_xml | – name: 2 Department of Mathematics, Lahore University of Management Sciences, Lahore Cantt., Pakistan – name: 1 Department of Mathematics, National College of Business Administration & Economics, Lahore Gulberg III, Pakistan – name: China University of Mining and Technology, CHINA |
| Author_xml | – sequence: 1 givenname: Amina orcidid: 0000-0002-6291-4671 surname: Amin fullname: Amin, Amina – sequence: 2 givenname: Imran surname: Naeem fullname: Naeem, Imran – sequence: 3 givenname: Adnan surname: Khan fullname: Khan, Adnan |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/36996046$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1016_j_rinp_2024_107454 |
| Cites_doi | 10.1016/j.ijleo.2016.09.055 10.1016/j.physleta.2007.07.051 10.1016/S0375-9601(98)00547-7 10.1016/j.cnsns.2016.06.017 10.1016/j.aml.2021.107290 10.1063/1.531282 10.1016/j.cam.2011.03.002 10.1016/j.amc.2010.03.071 10.1016/j.physleta.2005.05.085 10.1515/phys-2018-0042 10.1016/j.jde.2022.05.003 10.1007/978-1-4757-4307-4 10.1016/S0375-9601(02)00669-2 10.1016/S0375-9601(02)01516-5 10.1063/1.1334904 10.1016/j.amc.2006.06.043 10.1016/j.mcm.2003.12.010 10.1016/j.amc.2010.06.030 10.1016/j.amc.2003.08.136 10.1016/j.jmaa.2012.05.066 10.1016/j.physleta.2006.11.035 10.1016/S0375-9601(03)00196-8 10.1007/s12648-013-0401-6 10.1007/s11071-016-2998-4 10.1016/j.amc.2006.06.002 10.1007/978-1-4684-0274-2 10.1016/j.chaos.2006.03.039 10.1016/j.aim.2022.108639 |
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| Copyright | Copyright: © 2023 Amin 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 2023 Public Library of Science 2023 Amin 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. 2023 Amin et al 2023 Amin et al 2023 Amin 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. |
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| Snippet | The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional... |
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| SubjectTerms | Algorithms Applied mathematics Biology and Life Sciences Computer and Information Sciences Data mining Dependent variables Differential equations Engineering and Technology Evaluation Exact solutions Independent variables Nonlinear differential equations Nonlinear equations Partial differential equations Physical Sciences Physics Short Interspersed Nucleotide Elements Similarity Symmetry Trigonometric functions |
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| Title | Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations |
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