On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy

This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study p...

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Main Authors: Dilveen M. Ahmed, Bewar A. Mahmood, Ahmad Alalyani
Format: Article
Language:English
Published: Elsevier 2025-06-01
Series:Partial Differential Equations in Applied Mathematics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2666818125001111
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author Dilveen M. Ahmed
Bewar A. Mahmood
Ahmad Alalyani
author_facet Dilveen M. Ahmed
Bewar A. Mahmood
Ahmad Alalyani
author_sort Dilveen M. Ahmed
collection DOAJ
description This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields.
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institution Kabale University
issn 2666-8181
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series Partial Differential Equations in Applied Mathematics
spelling doaj-art-1bb7344955cf4a789e5761271ee8749c2025-08-20T03:53:17ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410118410.1016/j.padiff.2025.101184On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracyDilveen M. Ahmed0Bewar A. Mahmood1Ahmad Alalyani2Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Duhok, IraqDepartment of Mathematics, College of Science, University of Duhok, Kurdistan Region, Duhok, IraqDepartment of Mathematics, Faculty of Science, Al-Baha University, Al-Baha 65526, Saudi Arabia; Corresponding author.This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields.http://www.sciencedirect.com/science/article/pii/S2666818125001111Coupled Whitham–Broer–Kaup equationsVHPMNonlinear PDETraveling wave solutionVariational homotopy perturbation method
spellingShingle Dilveen M. Ahmed
Bewar A. Mahmood
Ahmad Alalyani
On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
Partial Differential Equations in Applied Mathematics
Coupled Whitham–Broer–Kaup equations
VHPM
Nonlinear PDE
Traveling wave solution
Variational homotopy perturbation method
title On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
title_full On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
title_fullStr On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
title_full_unstemmed On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
title_short On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
title_sort on the solution of the coupled whitham broer kaup problem using a hybrid technique for improved accuracy
topic Coupled Whitham–Broer–Kaup equations
VHPM
Nonlinear PDE
Traveling wave solution
Variational homotopy perturbation method
url http://www.sciencedirect.com/science/article/pii/S2666818125001111
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AT ahmadalalyani onthesolutionofthecoupledwhithambroerkaupproblemusingahybridtechniqueforimprovedaccuracy