One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation-Reference-Cited by-同舟云学术

One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation

Published:2021-11-23 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Paliathanasis Andronikos¹²^ORCID

Affiliation:

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

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

Abstract

Abstract We apply the Lie theory to determine the infinitesimal generators of the one-parameter point transformations which leave invariant the 3 + 1 Kudryashov–Sinelshchikov equation. We solve the classification problem of the one-dimensional optimal system, while we derive all the possible independent Lie invariants; that is, we determine all the independent similarity transformations which lead to different reductions. For an application, the results are applied to prove the existence of travel-wave solutions. Furthermore, the method of singularity analysis is applied where we show that the 3 + 1 Kudryashov–Sinelshchikov equation possess the Painlevé property and its solution can be written by using a Laurent expansion.

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-2020-0219/pdf

Reference50 articles.

1. P. J. Olver, Applications of Lie Groups to Differential Equations, New York, Springer-Verlag, 1993.

2. N. H. Ibragimov, “CRC handbook of lie group analysis of differential equations,” in Symmetries, Exact Solutions, and Conservation Laws, vol. I, Florida, CRS Press LLC, 2000.

3. G. W. Bluman and S. Kumei, Symmetries of Differential Equations, New York, Springer-Verlag, 1989.

4. H. Stephani, Differential Equations: Their Solutions Using Symmetry, New York, Cambridge University Press, 1989.

5. M. C. Nucci, “Jacobi’s last multiplier, Lie symmetries, and hidden linearity: “Goldfishes” galore,” Theor. Math. Phys., vol. 151, p. 851, 2007. https://doi.org/10.1007/s11232-007-0070-8.