Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations
A solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity during propagation, representing a fundamental phenomenon obs...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124000561 |
| _version_ | 1797220184049582080 |
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| author | Akhtar Hussain F.D. Zaman Hassan Ali |
| author_facet | Akhtar Hussain F.D. Zaman Hassan Ali |
| author_sort | Akhtar Hussain |
| collection | DOAJ |
| description | A solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity during propagation, representing a fundamental phenomenon observed widely in natural systems and possessing various applications in nonlinear dynamics. This investigation focuses on two nonlinear evolution equations (NEEs), specifically the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZKBBM) equation, which find relevance in domains such as fluid dynamics and ocean engineering. Utilizing an ansatz-based methodology, soliton solutions of both bright and dark characteristics are derived, alongside exploration of rogue wave-type solutions. Notably, the manifestation of dark, bright, and rogue waves aligns with the physical interpretation of the generated solitons. Computational simulations conducted using Wolfram Mathematica aim to provide a comprehensive description of the physical phenomena. The novelty of this study lies in its unreported investigation, contributing new insights into the solitonic dynamics within the considered models. |
| first_indexed | 2024-04-24T12:45:30Z |
| format | Article |
| id | doaj.art-23cec52f89264e71b4657d4181c53e58 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T12:45:30Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-23cec52f89264e71b4657d4181c53e582024-04-07T04:36:54ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-06-0110100670Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equationsAkhtar Hussain0F.D. Zaman1Hassan Ali2Corresponding author.; Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanA solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity during propagation, representing a fundamental phenomenon observed widely in natural systems and possessing various applications in nonlinear dynamics. This investigation focuses on two nonlinear evolution equations (NEEs), specifically the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZKBBM) equation, which find relevance in domains such as fluid dynamics and ocean engineering. Utilizing an ansatz-based methodology, soliton solutions of both bright and dark characteristics are derived, alongside exploration of rogue wave-type solutions. Notably, the manifestation of dark, bright, and rogue waves aligns with the physical interpretation of the generated solitons. Computational simulations conducted using Wolfram Mathematica aim to provide a comprehensive description of the physical phenomena. The novelty of this study lies in its unreported investigation, contributing new insights into the solitonic dynamics within the considered models.http://www.sciencedirect.com/science/article/pii/S2666818124000561Solitary wavesDispersive phenomenaNonlinear evolution equationsAnsatz approachDark and bright solitonsRogue waves |
| spellingShingle | Akhtar Hussain F.D. Zaman Hassan Ali Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations Partial Differential Equations in Applied Mathematics Solitary waves Dispersive phenomena Nonlinear evolution equations Ansatz approach Dark and bright solitons Rogue waves |
| title | Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations |
| title_full | Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations |
| title_fullStr | Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations |
| title_full_unstemmed | Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations |
| title_short | Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations |
| title_sort | dynamic nature of analytical soliton solutions of the nonlinear zkbbm and gzkbbm equations |
| topic | Solitary waves Dispersive phenomena Nonlinear evolution equations Ansatz approach Dark and bright solitons Rogue waves |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124000561 |
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