Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics
This research work explores fractional Dullin-Gottwald-Holm equation with Katugampola fractional derivatives via novel application of the generalized Riccati-Bernoulli sub-ODE approach in conjunction with the Bäcklund transformation. We develop fresh plethora of perturbed kink structures, kink and a...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-10-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447925003685 |
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| author | Yousef Jawarneh Ali H. Hakami Abaker A. Hassaballa |
| author_facet | Yousef Jawarneh Ali H. Hakami Abaker A. Hassaballa |
| author_sort | Yousef Jawarneh |
| collection | DOAJ |
| description | This research work explores fractional Dullin-Gottwald-Holm equation with Katugampola fractional derivatives via novel application of the generalized Riccati-Bernoulli sub-ODE approach in conjunction with the Bäcklund transformation. We develop fresh plethora of perturbed kink structures, kink and anti-kink soliton solutions using well-established criteria, and we evaluate their intricate behavior patterns. This study examines the impact of variations in the fractional-order parameter α on the soliton solutions through 2D graphical representations that reveal key insights into fractional-order effects. To illustrate the solitons' complex structure and formation, we combine contour plots with 3D graphs. This study advances our understanding of wave nonlinearity in complexly dynamic physical systems. Our work illustrates the influence of fractional parameters on solution behaviors, with broad implications for fluid mechanics and non-linear wave theory. This method's efficacy and adaptability show that it has the potential to tackle challenging non-linear problems and uncover a variety of fascinating physical phenomena. |
| format | Article |
| id | doaj-art-d56fb8957c19472b8bda5be7bfebe730 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-d56fb8957c19472b8bda5be7bfebe7302025-08-20T03:51:09ZengElsevierAin Shams Engineering Journal2090-44792025-10-01161010362710.1016/j.asej.2025.103627Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamicsYousef Jawarneh0Ali H. Hakami1Abaker A. Hassaballa2Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi ArabiaCenter for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia; Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia; Corresponding author.This research work explores fractional Dullin-Gottwald-Holm equation with Katugampola fractional derivatives via novel application of the generalized Riccati-Bernoulli sub-ODE approach in conjunction with the Bäcklund transformation. We develop fresh plethora of perturbed kink structures, kink and anti-kink soliton solutions using well-established criteria, and we evaluate their intricate behavior patterns. This study examines the impact of variations in the fractional-order parameter α on the soliton solutions through 2D graphical representations that reveal key insights into fractional-order effects. To illustrate the solitons' complex structure and formation, we combine contour plots with 3D graphs. This study advances our understanding of wave nonlinearity in complexly dynamic physical systems. Our work illustrates the influence of fractional parameters on solution behaviors, with broad implications for fluid mechanics and non-linear wave theory. This method's efficacy and adaptability show that it has the potential to tackle challenging non-linear problems and uncover a variety of fascinating physical phenomena.http://www.sciencedirect.com/science/article/pii/S2090447925003685Fractional Dullin-Gottwald-Holm (DGH) equationGeneralized Riccati-Bernoulli sub-ODE methodSolitary wave solutionNon-linear partial differential equations (PDEs) |
| spellingShingle | Yousef Jawarneh Ali H. Hakami Abaker A. Hassaballa Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics Ain Shams Engineering Journal Fractional Dullin-Gottwald-Holm (DGH) equation Generalized Riccati-Bernoulli sub-ODE method Solitary wave solution Non-linear partial differential equations (PDEs) |
| title | Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics |
| title_full | Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics |
| title_fullStr | Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics |
| title_full_unstemmed | Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics |
| title_short | Generalized analysis of fractional Dullin-Gottwald-Holm equation: Soliton solutions and their applications in non-linear wave dynamics |
| title_sort | generalized analysis of fractional dullin gottwald holm equation soliton solutions and their applications in non linear wave dynamics |
| topic | Fractional Dullin-Gottwald-Holm (DGH) equation Generalized Riccati-Bernoulli sub-ODE method Solitary wave solution Non-linear partial differential equations (PDEs) |
| url | http://www.sciencedirect.com/science/article/pii/S2090447925003685 |
| work_keys_str_mv | AT yousefjawarneh generalizedanalysisoffractionaldullingottwaldholmequationsolitonsolutionsandtheirapplicationsinnonlinearwavedynamics AT alihhakami generalizedanalysisoffractionaldullingottwaldholmequationsolitonsolutionsandtheirapplicationsinnonlinearwavedynamics AT abakerahassaballa generalizedanalysisoffractionaldullingottwaldholmequationsolitonsolutionsandtheirapplicationsinnonlinearwavedynamics |