Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation
The Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component...
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| Format: | Article |
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Wiley
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/9996101 |
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| author | Sheng Zhang Feng Zhu Bo Xu |
| author_facet | Sheng Zhang Feng Zhu Bo Xu |
| author_sort | Sheng Zhang |
| collection | DOAJ |
| description | The Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. In addition, we find that the dominant role of fractional order leads to new dynamic characteristics of the obtained fractional soliton and semirational solutions, mainly including a certain degree of tilt of wave crests and the variations in velocities and wave widths over time during propagation, which are not possessed by the corresponding integer-order TCGH equation. Meanwhile, this study predicts the deceleration propagation of solitons in fractional dimensional media and brings the possibility of exploring the asymmetric regulation mechanism of rogue waves from the perspective of fractional-order dominance. |
| format | Article |
| id | doaj-art-1e964c864ffe44b59c7409457246d93a |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-1e964c864ffe44b59c7409457246d93a2025-02-03T06:45:13ZengWileyAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/9996101Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota EquationSheng Zhang0Feng Zhu1Bo Xu2School of Mathematical SciencesSchool of Mathematical SciencesSchool of Educational SciencesThe Darboux transformation (DT) and generalized DT (GDT) have played important roles in constructing multisoliton solutions, rogue wave solutions, and semirational solutions of integrable systems. The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. In addition, we find that the dominant role of fractional order leads to new dynamic characteristics of the obtained fractional soliton and semirational solutions, mainly including a certain degree of tilt of wave crests and the variations in velocities and wave widths over time during propagation, which are not possessed by the corresponding integer-order TCGH equation. Meanwhile, this study predicts the deceleration propagation of solitons in fractional dimensional media and brings the possibility of exploring the asymmetric regulation mechanism of rogue waves from the perspective of fractional-order dominance.http://dx.doi.org/10.1155/2023/9996101 |
| spellingShingle | Sheng Zhang Feng Zhu Bo Xu Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation Advances in Mathematical Physics |
| title | Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation |
| title_full | Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation |
| title_fullStr | Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation |
| title_full_unstemmed | Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation |
| title_short | Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation |
| title_sort | fractional soliton and semirational solutions of a fractional two component generalized hirota equation |
| url | http://dx.doi.org/10.1155/2023/9996101 |
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