RESEARCH PAPER
Approximate Solution of Painlevé Equation I by Natural Decomposition Method and Laplace Decomposition Method
1
Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
2
Department of Mathematics, University of Management and Technology Lahore, Pakistan
Submission date: 2022-12-08
Acceptance date: 2023-03-19
Online publication date: 2023-07-15
Publication date: 2023-09-01
Acta Mechanica et Automatica 2023;17(3):417-422
KEYWORDS
natural decomposition methodLaplace decomposition methodseries solutionAdomain polynomialPainlevéequation
ABSTRACT
Novelty:
One of the key novelties of the Painlevé equations is their remarkable property of having only movable singularities, which means that their solutions do not have any singularities that are fixed in position. This property makes the Painlevé equations particularly useful in the study of non-linear systems, as it allows for the construction of exact solutions in certain cases. Another important feature of the Painlevé equations is their appearance in diverse fields such as statistical mechanics, random matrix theory and soliton theory. This has led to a wide range of applications, including the study of random processes, the dynamics of fluids and the behaviour of non-linear waves.
One of the key novelties of the Painlevé equations is their remarkable property of having only movable singularities, which means that their solutions do not have any singularities that are fixed in position. This property makes the Painlevé equations particularly useful in the study of non-linear systems, as it allows for the construction of exact solutions in certain cases. Another important feature of the Painlevé equations is their appearance in diverse fields such as statistical mechanics, random matrix theory and soliton theory. This has led to a wide range of applications, including the study of random processes, the dynamics of fluids and the behaviour of non-linear waves.
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| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
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