Lie symmetries and singularity analysis for generalized shallow-water equations-Reference-Cited by-同舟云学术

Lie symmetries and singularity analysis for generalized shallow-water equations

Published:2020-08-10 Issue:7-8 Volume:21 Page:739-747
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Paliathanasis Andronikos¹²

Affiliation:

1. Institute of Systems Science , Durban University of Technology , PO Box 1334 , Durban, 4000 , Republic of South Africa

2. Instituto de Ciencias Físicas y Matemáticas , Universidad Austral de Chile , Valdivia, 5090000 , Chile

Abstract

Abstract We perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized Benjamin-Bono-Mahoney (BBM) equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the CH equation. We determine the one-dimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the similarity solutions for the two equations of our study. The reduced equations are studied by using the point symmetries or the singularity analysis. Finally, the singularity analysis is directly applied on the partial differential equations from where we infer that the generalized equations of our study pass the singularity test and are integrable.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2019-0152/pdf

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