Lie algebra classification, conservation laws and invariant solutions for the a particular case of the generalized Levinson-Smith equation

Yeisson Alexis Acevedo Agudelo; Gabriel Ignacio Loaiza Ossa; Oscar Mario  Londoño Duque; Danilo A.  García Hernández

doi:10.22517/23447214.24960

Lie algebra classification, conservation laws and invariant solutions for the a particular case of the generalized Levinson-Smith equation

Authors

Yeisson Alexis Acevedo Agudelo Universidad EAFIT https://orcid.org/0000-0002-1640-9084
Gabriel Ignacio Loaiza Ossa Universidad EAFIT https://orcid.org/0000-0003-2413-1139
Oscar Mario Londoño Duque Universidad EAFIT https://orcid.org/0000-0002-5666-8224
Danilo A. García Hernández Universidade Estadual de Campinas, Brazil https://orcid.org/0000-0002-0807-2602

DOI:

https://doi.org/10.22517/23447214.24960

Keywords:

Invariant solutions, Lie symmetry group, Optimal system, Lie algebra classification, Variational symmetries, Conservation laws, Noether’s theorem

Abstract

In this study, we examine a specific instance of the generalized Levinson-Smith equation, which is linked to the Liènard equation and holds significant importance from the perspectives of physics, mathematics, and engineering. This underlying equation has practical applications in mechanics and nonlinear dynamics and has been extensively explored in the qualitative scheme. Our approach involves applying the Lie group method to this equation. By doing so, we derive the optimal generating operators for the system that pertain to the specific instance of the generalized Levinson-Smith equation. These operators are then used to define all invariant solutions associated with the equation. In addition, we demonstrate the variational symmetries and corresponding conservation laws using Noether's theorem. Finally, we categorize the Lie algebra related to the given equation.

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Published

2023-06-30

How to Cite

Acevedo Agudelo, Y. A., Loaiza Ossa, G. I., Londoño Duque, O. M. ., & García Hernández, D. A. . (2023). Lie algebra classification, conservation laws and invariant solutions for the a particular case of the generalized Levinson-Smith equation. Scientia Et Technica, 28(02). https://doi.org/10.22517/23447214.24960

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Issue

Vol. 28 No. 02 (2023): Abril-Junio

Section

Ciencias Básicas

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