Novel wave solutions for the sixth-order Boussinesq equation arising in nonlinear lattice dynamics

Ali Althobaiti; Ali Althobaiti

doi:10.3934/math.20241494

AIMS Mathematics

2024, Volume 9, Issue 11: 30972-30988. doi: 10.3934/math.20241494

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Novel wave solutions for the sixth-order Boussinesq equation arising in nonlinear lattice dynamics

Ali Althobaiti ^,

Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 29 July 2024 Revised: 12 September 2024 Accepted: 15 October 2024 Published: 31 October 2024
MSC : 35A09, 35A24, 35C07, 35C08

This study examines a class of Boussinesq equations with sixth-order using two promising analytical methods. The equation in question is among the frontier evolution equations with significant relevance in nonlinear lattice dynamics. To study this model, the Kudryashov method and the modified auxiliary equation method are employed due to their analytical precision in constructing several exact wave solutions for the model under examination. As expected, the methods yield many valid solution sets that satisfy all the underlying assumptions of the model. Finally, some of the obtained wave solutions are graphically illustrated, taking into account the parameter values of the model.
- higher-order evolution equations,
- Boussinesq equation,
- exact wave solutions,
- Kudryashov method,
- modified auxiliary equation method
Citation: Ali Althobaiti. Novel wave solutions for the sixth-order Boussinesq equation arising in nonlinear lattice dynamics[J]. AIMS Mathematics, 2024, 9(11): 30972-30988. doi: 10.3934/math.20241494

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Abstract

This study examines a class of Boussinesq equations with sixth-order using two promising analytical methods. The equation in question is among the frontier evolution equations with significant relevance in nonlinear lattice dynamics. To study this model, the Kudryashov method and the modified auxiliary equation method are employed due to their analytical precision in constructing several exact wave solutions for the model under examination. As expected, the methods yield many valid solution sets that satisfy all the underlying assumptions of the model. Finally, some of the obtained wave solutions are graphically illustrated, taking into account the parameter values of the model.

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