Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature.
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| Title: | Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature. |
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| Authors: | Roshid, Md. Mamunur1 (AUTHOR) mamunmath@hamdarduniversity.edu.bd, Hafez, Ramy M.2 (AUTHOR), Uddin, Mahtab3 (AUTHOR), Yildirim, Yakup4,5 (AUTHOR), Mostafa, Golam6 (AUTHOR) golam.mostafa@seu.edu.bd, Da-Wei, Zuo (AUTHOR) daweizuo@stdu.edu.cn |
| Source: | Journal of Applied Mathematics. 6/5/2026, Vol. 2026, p1-14. 14p. |
| Subjects: | Solitons, Modulational instability, Stochastic partial differential equations, Signal-to-noise ratio, Traveling waves (Physics), Chaos theory, Shock waves, Partial differential equations |
| Abstract: | This study investigates the stochastic fractional new coupled Konno–Oono equation with external forced multiplicative noise, focusing on the chaotic nature, the influence of multiplicative noise intensity, and the fractionality parameter on exact soliton solutions. The proposed model is used to describe the complex phenomena in the magnetic field. To examine the exact solutions for the stochastic fractional new coupled Konno–Oono equation, the functional transformation method is applied. This method yields various forms of travelling wave solutions, including Jacobian elliptic, exponential, hyperbolic, and trigonometric functions, each dependent on different parameters. Additionally, we investigate the quasiperiodic and chaotic behavior of the system, including the formation of shock wave structures and sensitivity to initial conditions. The modulation instability is also investigated for the proposed model, which is important for quickly creating localized structures (such as solitons or rogue waves) by destabilizing unbroken waves when they are slightly disturbed, allowing for energy localization and spectrum widening. The findings in this study not only broaden but also enhance certain results from earlier research. Moreover, the influence of multiplicative noise on the analytical solutions of the stochastic system is illustrated through 3D diagrams and corresponding 2D path lines. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194361622 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Roshid%2C+Md%2E+Mamunur%22">Roshid, Md. Mamunur</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mamunmath@hamdarduniversity.edu.bd</i><br /><searchLink fieldCode="AR" term="%22Hafez%2C+Ramy+M%2E%22">Hafez, Ramy M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Uddin%2C+Mahtab%22">Uddin, Mahtab</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yildirim%2C+Yakup%22">Yildirim, Yakup</searchLink><relatesTo>4,5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mostafa%2C+Golam%22">Mostafa, Golam</searchLink><relatesTo>6</relatesTo> (AUTHOR)<i> golam.mostafa@seu.edu.bd</i><br /><searchLink fieldCode="AR" term="%22Da-Wei%2C+Zuo%22">Da-Wei, Zuo</searchLink> (AUTHOR)<i> daweizuo@stdu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 6/5/2026, Vol. 2026, p1-14. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink><br /><searchLink fieldCode="DE" term="%22Modulational+instability%22">Modulational instability</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+partial+differential+equations%22">Stochastic partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Signal-to-noise+ratio%22">Signal-to-noise ratio</searchLink><br /><searchLink fieldCode="DE" term="%22Traveling+waves+%28Physics%29%22">Traveling waves (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Shock+waves%22">Shock waves</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study investigates the stochastic fractional new coupled Konno–Oono equation with external forced multiplicative noise, focusing on the chaotic nature, the influence of multiplicative noise intensity, and the fractionality parameter on exact soliton solutions. The proposed model is used to describe the complex phenomena in the magnetic field. To examine the exact solutions for the stochastic fractional new coupled Konno–Oono equation, the functional transformation method is applied. This method yields various forms of travelling wave solutions, including Jacobian elliptic, exponential, hyperbolic, and trigonometric functions, each dependent on different parameters. Additionally, we investigate the quasiperiodic and chaotic behavior of the system, including the formation of shock wave structures and sensitivity to initial conditions. The modulation instability is also investigated for the proposed model, which is important for quickly creating localized structures (such as solitons or rogue waves) by destabilizing unbroken waves when they are slightly disturbed, allowing for energy localization and spectrum widening. The findings in this study not only broaden but also enhance certain results from earlier research. Moreover, the influence of multiplicative noise on the analytical solutions of the stochastic system is illustrated through 3D diagrams and corresponding 2D path lines. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/jama/7600408 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 1 Subjects: – SubjectFull: Solitons Type: general – SubjectFull: Modulational instability Type: general – SubjectFull: Stochastic partial differential equations Type: general – SubjectFull: Signal-to-noise ratio Type: general – SubjectFull: Traveling waves (Physics) Type: general – SubjectFull: Chaos theory Type: general – SubjectFull: Shock waves Type: general – SubjectFull: Partial differential equations Type: general Titles: – TitleFull: Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Roshid, Md. Mamunur – PersonEntity: Name: NameFull: Hafez, Ramy M. – PersonEntity: Name: NameFull: Uddin, Mahtab – PersonEntity: Name: NameFull: Yildirim, Yakup – PersonEntity: Name: NameFull: Mostafa, Golam – PersonEntity: Name: NameFull: Da-Wei, Zuo IsPartOfRelationships: – BibEntity: Dates: – D: 05 M: 06 Text: 6/5/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
| ResultId | 1 |
