Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions

Nauman Raza; Maria Luz Gandarias; Ghada Ali Basendwah; Nauman Raza; Maria Luz Gandarias; Ghada Ali Basendwah

doi:10.3934/math.2024503

AIMS Mathematics

2024, Volume 9, Issue 4: 10289-10303. doi: 10.3934/math.2024503

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Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions

1.
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan
2.
Department of Mathematics, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey
3.
Department of Mathematics, University of Cadiz, Puerto Real, Cádiz 11510, Spain
4.
Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 20 December 2023 Revised: 26 February 2024 Accepted: 04 March 2024 Published: 14 March 2024
MSC : 35B32, 35C08

This article represented the investigation of the modified mixed Korteweg-de Vries equation using different versatile approaches. First, the Lie point symmetry approach was used to determine all possible symmetry generators. With the help of these generators, we reduced the dimension of the proposed equation which leads to the ordinary differential equation. Second, we employed the unified Riccati equation expansion technique to construct the abundance of soliton dynamics. A group of kink solitons and other solitons related to hyperbolic functions were among these solutions. To give the physical meaning of these theoretical results, we plotted these solutions in 3D, contour, and 2D graphs using suitable physical parameters. The comprehend outcomes were reported, which can be useful and beneficial in the future investigation of the studied equation. The results showed that applied techniques are very useful to study the other nonlinear physical problems in nonlinear sciences.
- symmetry reductions,
- invariant solution,
- unified Riccati equation expansion method,
- exact solution,
- modified mixed KdV equation
Citation: Nauman Raza, Maria Luz Gandarias, Ghada Ali Basendwah. Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions[J]. AIMS Mathematics, 2024, 9(4): 10289-10303. doi: 10.3934/math.2024503

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Abstract

This article represented the investigation of the modified mixed Korteweg-de Vries equation using different versatile approaches. First, the Lie point symmetry approach was used to determine all possible symmetry generators. With the help of these generators, we reduced the dimension of the proposed equation which leads to the ordinary differential equation. Second, we employed the unified Riccati equation expansion technique to construct the abundance of soliton dynamics. A group of kink solitons and other solitons related to hyperbolic functions were among these solutions. To give the physical meaning of these theoretical results, we plotted these solutions in 3D, contour, and 2D graphs using suitable physical parameters. The comprehend outcomes were reported, which can be useful and beneficial in the future investigation of the studied equation. The results showed that applied techniques are very useful to study the other nonlinear physical problems in nonlinear sciences.

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