Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation.
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| Title: | Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation. |
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| Authors: | Wu, Zhi‐Jia1 (AUTHOR), Tian, Shou‐Fu1 (AUTHOR) sftian@cumt.edu.cn |
| Source: | Studies in Applied Mathematics. Nov2024, Vol. 153 Issue 4, p1-38. 38p. |
| Subjects: | Riemann-Hilbert problems, Modulation theory, Elliptic functions, Shock waves, Velocity |
| Abstract: | In this work, we explore the Riemann problem of the Fokas–Lenells (FL) equation given initial data in the form of a step discontinuity by employing the Whitham modulation theory. The periodic wave solutions of the FL equation are characterized by elliptic functions along with the Whitham modulation equations. Moreover, we find that the ±$\pm$ signs for the velocities of the periodic wave solutions remain unchanged during propagation. Thus, when analyzing the propagation behavior of solutions, it is necessary to separately consider the clockwise (negative velocity) and counterclockwise (positive velocity) cases. In this regard, we present the classification of the solutions to the Riemann problem of the FL equation in both clockwise and counterclockwise cases for the first time. [ABSTRACT FROM AUTHOR] |
| Copyright of Studies in 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: 180736968 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wu%2C+Zhi‐Jia%22">Wu, Zhi‐Jia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tian%2C+Shou‐Fu%22">Tian, Shou‐Fu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sftian@cumt.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Studies+in+Applied+Mathematics%22">Studies in Applied Mathematics</searchLink>. Nov2024, Vol. 153 Issue 4, p1-38. 38p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Riemann-Hilbert+problems%22">Riemann-Hilbert problems</searchLink><br /><searchLink fieldCode="DE" term="%22Modulation+theory%22">Modulation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+functions%22">Elliptic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Shock+waves%22">Shock waves</searchLink><br /><searchLink fieldCode="DE" term="%22Velocity%22">Velocity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we explore the Riemann problem of the Fokas–Lenells (FL) equation given initial data in the form of a step discontinuity by employing the Whitham modulation theory. The periodic wave solutions of the FL equation are characterized by elliptic functions along with the Whitham modulation equations. Moreover, we find that the ±$\pm$ signs for the velocities of the periodic wave solutions remain unchanged during propagation. Thus, when analyzing the propagation behavior of solutions, it is necessary to separately consider the clockwise (negative velocity) and counterclockwise (positive velocity) cases. In this regard, we present the classification of the solutions to the Riemann problem of the FL equation in both clockwise and counterclockwise cases for the first time. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Studies in 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: 10.1111/sapm.12779 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 1 Subjects: – SubjectFull: Riemann-Hilbert problems Type: general – SubjectFull: Modulation theory Type: general – SubjectFull: Elliptic functions Type: general – SubjectFull: Shock waves Type: general – SubjectFull: Velocity Type: general Titles: – TitleFull: Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wu, Zhi‐Jia – PersonEntity: Name: NameFull: Tian, Shou‐Fu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00222526 Numbering: – Type: volume Value: 153 – Type: issue Value: 4 Titles: – TitleFull: Studies in Applied Mathematics Type: main |
| ResultId | 1 |
