<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary application. Given the wide application of classical Lie symmetry methods in this field, this study employs a Lie symmetry analysis to investigate the CZK equations, as detailed in this research. Our methodology involves the construction of a nine-dimensional optimal system by leveraging the fundamental elements of the Lie algebra. Subsequently, we apply similarity reductions to the equations using each subalgebra. The resulting invariant solutions find diverse applications within the realm of physics and can also be adapted to solve a broad range of related nonlinear evolution equations. We meticulously validate all these solutions through a straightforward verification process. To enhance our comprehension of the physical implications of these solutions, we employ Mathematica simulations to visually represent various solution scenarios. Additionally, to preserve conservation laws, we incorporate Ibragimov’s novel conservation law theorem as a crucial component of our analysis.</p>
</abstract>

This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary application. Given the wide application of classical Lie symmetry methods in this field, this study employs a Lie symmetry analysis to investigate the CZK equations, as detailed in this research. Our methodology involves the construction of a nine-dimensional optimal system by leveraging the fundamental elements of the Lie algebra. Subsequently, we apply similarity reductions to the equations using each subalgebra. The resulting invariant solutions find diverse applications within the realm of physics and can also be adapted to solve a broad range of related nonlinear evolution equations. We meticulously validate all these solutions through a straightforward verification process. To enhance our comprehension of the physical implications of these solutions, we employ Mathematica simulations to visually represent various solution scenarios. Additionally, to preserve conservation laws, we incorporate Ibragimov’s novel conservation law theorem as a crucial component of our analysis.

Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

College of Electrical and Mechanical Engineering

National University of Science and Technology

Abdus Salam School of Mathematical Sciences

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK)...

[Q_i,Q_j]	Q₁	Q₂	Q₃	Q₄

Q₁	Q₁	Q₂	Q₃	Q₄ − ɛQ₂
Q₂	Q₁	Q₂	Q₃	Q₄
Q₃	Q₁	Q₂	Q₃	Q₄
Q₄	Q₁ + ɛQ₂	Q₂	Q₃	Q₄

[Q_i,Q_j]	Q₁	Q₂	Q₃	Q₄

Q₁	0	0	0	Q₂
Q₂	0	0	0	0
Q₃	0	0	0	0
Q₄	−Q₂	0	0	0

Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

Article Category: Original Study

Publié en ligne: 10 janv. 2024

Pages: 193 - 210

Reçu: 18 août 2023

Accepté: 13 nov. 2023

DOI: https://doi.org/10.2478/ijmce-2024-0015

Mots clés
Classical Lie symmetry method, CZK equations, sub-algebra, optimal system, Mathematica simulations

© 2024 Muhammad Usman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Adjoint table.

Commutator table.

Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

Article Category: Original Study

Publié en ligne: 10 janv. 2024

Pages: 193 - 210

Reçu: 18 août 2023

Accepté: 13 nov. 2023

DOI: https://doi.org/10.2478/ijmce-2024-0015

Mots clésClassical Lie symmetry method, CZK equations, sub-algebra, optimal system, Mathematica simulations

© 2024 Muhammad Usman et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Adjoint table.

Commutator table.

Mots clés
Classical Lie symmetry method, CZK equations, sub-algebra, optimal system, Mathematica simulations