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Journals
International Journal of Mathematics and Computer in Engineering
Volume 2 (2024): Issue 2 (December 2024)
Open Access
Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra
Muhammad Usman
Muhammad Usman
,
Akhtar Hussain
Akhtar Hussain
,
Fiazuddin Zaman
Fiazuddin Zaman
and
Naseem Abbas
Naseem Abbas
| Jan 10, 2024
International Journal of Mathematics and Computer in Engineering
Volume 2 (2024): Issue 2 (December 2024)
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Article Category:
Original Study
Published Online:
Jan 10, 2024
Page range:
193 - 210
Received:
Aug 18, 2023
Accepted:
Nov 13, 2023
DOI:
https://doi.org/10.2478/ijmce-2024-0015
Keywords
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
Structural dynamics of (1) by (42) when all parameters are set to 1 and at t = 1,2,3.
Fig. 2
Structural dynamics of (1) by (44) when all parameters are set to 1 and at t = 1,2,3.
Fig. 3
Structural dynamics of (1) by (52) when all parameters are set to 1 and at t = 1,2,3.
Fig. 4
Structural dynamics of (1) by (54) when all parameters are set to 1 and at t = 1,2,3.
Fig. 5
Periodic dynamics of (1) by (56) when all parameters are set to 1 and at t = 1,2,3.
Fig. 6
Periodic dynamics of (1) by (56) when all parameters are set to 1 and at t = 1,2,3.
Fig. 7
Structural dynamics of (1) by (66) when all parameters are set to 1 and at t = 1,2,3.
Fig. 8
Structural dynamics of (1) by (66) when all parameters are set to 1 and at aα5 = −1, t = 1,2,3.
Adjoint table.
[
Q
i
,Q
j
]
Q
1
Q
2
Q
3
Q
4
Q
1
Q
1
Q
2
Q
3
Q
4
−
ɛQ
2
Q
2
Q
1
Q
2
Q
3
Q
4
Q
3
Q
1
Q
2
Q
3
Q
4
Q
4
Q
1
+
ɛQ
2
Q
2
Q
3
Q
4
Commutator table.
[
Q
i
,
Q
j
]
Q
1
Q
2
Q
3
Q
4
Q
1
0
0
0
Q
2
Q
2
0
0
0
0
Q
3
0
0
0
0
Q
4
−
Q
2
0
0
0