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 inPloS one Vol. 18; no. 3; p. e0283569
Main Authors Amin, Amina, Naeem, Imran, Khan, Adnan
Format Journal Article
LanguageEnglish
Published United States Public Library of Science 30.03.2023
Public Library of Science (PLoS)
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ISSN1932-6203
1932-6203
DOI10.1371/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.
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
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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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StartPage e0283569
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
URI https://www.ncbi.nlm.nih.gov/pubmed/36996046
https://www.proquest.com/docview/2792881981
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https://pubmed.ncbi.nlm.nih.gov/PMC10062672
https://doi.org/10.1371/journal.pone.0283569
https://doaj.org/article/840745860c954a6da78d7f3d215bb298
http://dx.doi.org/10.1371/journal.pone.0283569
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