The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions-Reference-Cited by-同舟云学术

The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions

Published:2021-11-26 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Akbulut Arzu¹^ORCID,Rezazadeh Hadi²,Hashemi Mir Sajjad³^ORCID,Taşcan Filiz¹

Affiliation:

1. Department of Mathematics – Computer , Eskişehir Osmangazi University, Art-Science Faculty , Eskişehir , Turkey

2. Faculty of Engineering Technology , Amol University of Special Modern Technologies , Amol , Iran

3. Department of Mathematics, Basic Science Faculty , University of Bonab , P.O. Box 55513-95133 , Bonab , Iran

Abstract

Abstract In this study, we dealt with the new conservation theorem and the auxiliary method. We have applied the theorem and method to (3 + 1)-dimensional modified Wazwaz–KdV equations. When we applied a new conservation theorem to given equations, the obtained conservation laws did not satisfy the divergence condition. So, we modified the obtained conservation laws. These conservation laws contain extra terms. Finally, we applied the auxiliary method to given equations. We obtained two solution families with six exact solutions. All the obtained solutions are different from each other. For a suitable value of the solutions, the 3D and 2D surfaces have been plotted by Maple.

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-2021-0161/pdf

Reference55 articles.

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

2. F. Tascan and A. Yakut, “Conservation laws and exact solutions with symmetry reduction of nonlinear reaction diffusion equations,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 16, nos. 3–4, pp. 191–196, 2015. https://doi.org/10.1515/ijnsns-2014-0098.

3. M. S. Hashemi and D. Baleanu, Lie Symmetry Analysis of Fractional Differential Equations, Boca Raton, CRC Press, 2020.

4. M. S. Hashemi, E. Darvishi, and D. Baleanu, “A geometric approach for solving the density-dependent diffusion Nagumo equation,” Adv. Differ. Equ., vol. 2016, no. 1, pp. 1–13, 2016. https://doi.org/10.1186/s13662-016-0818-2.

5. M. S. Hashemi and Z. Balmeh, “On invariant analysis and conservation laws of the time fractional variant Boussinesq and coupled Boussinesq–Burger’s equations,” Eur. Phys. J. Plus, vol. 133, no. 10, pp. 1–11, 2018. https://doi.org/10.1140/epjp/i2018-12289-1.

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