Lie symmetry, numerical solution with spectral method and conservation laws of Degasperis-Procesi equation by homotopy and direct methods

Partial differential equations are widely used to describe complex phenomena in various branches of science, including: physics, mechanics, etc. Therefore, obtaining high-precision target solutions and, if possible, finding exact analytical solutions of these equations play an important role in thes...

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Bibliographic Details
Published in:International journal of modelling & simulation 2024-03, Vol.44 (2), p.61-76
Main Authors: Hejazi, S. Reza, Mohammadi, Shaban
Format: Article
Language:English
Subjects:
Combinations (mathematics)
conservation law
Conservation laws
Exact solutions
homotopy
invariant transformations
Invariants
Lie symmetry
Partial differential equations
Similarity solutions
spectral method
Spectral methods
Symmetry
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Summary:Partial differential equations are widely used to describe complex phenomena in various branches of science, including: physics, mechanics, etc. Therefore, obtaining high-precision target solutions and, if possible, finding exact analytical solutions of these equations play an important role in these sciences. In this paper, we first examine Lie symmetry and invariant transformations. Next, we obtain the equation solutions with the help of symmetries. We compute invariants and similarity solutions. Spectral method was used to numerically solve the equation. Then, we introduce two approaches, the Homotopy method and the direct method, which are used to construct conservation laws. Then we construct three conservation laws for the Degasperis-Procesi equation by using the direct method. Numerical solution and analysis of the Degasperis-Procesi equation by the methods proposed in this research have not been done in previous studies. Also, in Iran, this is the first time that this research has been done, which is a combination of mathematics, physics and computer science, and is considered interdisciplinary and applied.
ISSN:0228-6203
1925-7082
DOI:10.1080/02286203.2022.2155774