The analytical solutions of the Sharma–Tasso–Olver–Burgers equation using improved sub-equation method.
Saved in:
| Title: | The analytical solutions of the Sharma–Tasso–Olver–Burgers equation using improved sub-equation method. |
|---|---|
| Authors: | Arslantürk, Reyhan1 (AUTHOR) reyhanarslanturk52@gmail.com, Durur, Hülya2 (AUTHOR) hulyadurur@ardahan.edu.tr |
| Source: | Modern Physics Letters B. 5/10/2026, Vol. 40 Issue 13, p1-24. 24p. |
| Subjects: | Analytical solutions, Nonlinear evolution equations, Traveling waves (Physics), Solitons, Plasma physics, Shock waves, Fluid mechanics |
| Abstract: | In this study, various traveling wave solutions of the Sharma–Tasso–Olver–Burgers (STOB) equation were obtained using the improved sub-equation method in order to achieve traveling wave solutions of nonlinear evolution equations. The STOB equation, derived from the combination of the Burgers equation and the Sharma–Tasso–Olver equation, is a solvable model that examines the interaction between nonlinear convection and diffusion processes. This equation is an important tool for describing soliton, shock, and complex wave structures that occur in fields such as fluid mechanics, plasma physics, nonlinear optics, and quantum field theory. In the study, the improved sub-equation method, which is an extended form of the classical sub-equation method, was used; through this method, not only positive power terms but also inverse power components were included in the solution space. Within this framework, sixteen different traveling wave solutions based on hyperbolic and trigonometric functions such as tanh, coth, tan, and cot were obtained. The obtained solutions represent different physical behaviors, such as kink-type solitons, periodic waves, complex structures containing singularities, and rational waves, depending on the system parameters. As a result of graphical analyses, it was determined that the characteristics of the solutions, such as amplitude, velocity, and frequency, are directly related to the system parameters. In three-dimensional (3D), two-dimensional (2D), and contour plots, it was observed that the wave profiles exhibit significant energy concentrations in resonance regions. This provides important information for modeling sudden distortions, energy accumulation, and resonance processes in fields such as optics, fluid mechanics, and plasma physics. The developed solutions expanded the solution space of the STOB equation, and the method has emerged as a powerful, systematic, and generalizable tool for the analytical investigation of nonlinear systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Modern Physics Letters B is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 192969251 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: The analytical solutions of the Sharma–Tasso–Olver–Burgers equation using improved sub-equation method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Arslantürk%2C+Reyhan%22">Arslantürk, Reyhan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> reyhanarslanturk52@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Durur%2C+Hülya%22">Durur, Hülya</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hulyadurur@ardahan.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Modern+Physics+Letters+B%22">Modern Physics Letters B</searchLink>. 5/10/2026, Vol. 40 Issue 13, p1-24. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+evolution+equations%22">Nonlinear evolution equations</searchLink><br /><searchLink fieldCode="DE" term="%22Traveling+waves+%28Physics%29%22">Traveling waves (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink><br /><searchLink fieldCode="DE" term="%22Plasma+physics%22">Plasma physics</searchLink><br /><searchLink fieldCode="DE" term="%22Shock+waves%22">Shock waves</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+mechanics%22">Fluid mechanics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this study, various traveling wave solutions of the Sharma–Tasso–Olver–Burgers (STOB) equation were obtained using the improved sub-equation method in order to achieve traveling wave solutions of nonlinear evolution equations. The STOB equation, derived from the combination of the Burgers equation and the Sharma–Tasso–Olver equation, is a solvable model that examines the interaction between nonlinear convection and diffusion processes. This equation is an important tool for describing soliton, shock, and complex wave structures that occur in fields such as fluid mechanics, plasma physics, nonlinear optics, and quantum field theory. In the study, the improved sub-equation method, which is an extended form of the classical sub-equation method, was used; through this method, not only positive power terms but also inverse power components were included in the solution space. Within this framework, sixteen different traveling wave solutions based on hyperbolic and trigonometric functions such as tanh, coth, tan, and cot were obtained. The obtained solutions represent different physical behaviors, such as kink-type solitons, periodic waves, complex structures containing singularities, and rational waves, depending on the system parameters. As a result of graphical analyses, it was determined that the characteristics of the solutions, such as amplitude, velocity, and frequency, are directly related to the system parameters. In three-dimensional (3D), two-dimensional (2D), and contour plots, it was observed that the wave profiles exhibit significant energy concentrations in resonance regions. This provides important information for modeling sudden distortions, energy accumulation, and resonance processes in fields such as optics, fluid mechanics, and plasma physics. The developed solutions expanded the solution space of the STOB equation, and the method has emerged as a powerful, systematic, and generalizable tool for the analytical investigation of nonlinear systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Modern Physics Letters B is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192969251 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S021798492650082X Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 1 Subjects: – SubjectFull: Analytical solutions Type: general – SubjectFull: Nonlinear evolution equations Type: general – SubjectFull: Traveling waves (Physics) Type: general – SubjectFull: Solitons Type: general – SubjectFull: Plasma physics Type: general – SubjectFull: Shock waves Type: general – SubjectFull: Fluid mechanics Type: general Titles: – TitleFull: The analytical solutions of the Sharma–Tasso–Olver–Burgers equation using improved sub-equation method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Arslantürk, Reyhan – PersonEntity: Name: NameFull: Durur, Hülya IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 05 Text: 5/10/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02179849 Numbering: – Type: volume Value: 40 – Type: issue Value: 13 Titles: – TitleFull: Modern Physics Letters B Type: main |
| ResultId | 1 |
