Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example
Joint Authors
Xu, Bo
Wei, Yuanyuan
Zhang, Sheng
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-06
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In this paper, the spectral transform with the reputation of nonlinear Fourier transform is extended for the first time to a local time-fractional Korteweg-de vries (tfKdV) equation.
More specifically, a linear spectral problem associated with the KdV equation of integer order is first equipped with local time-fractional derivative.
Based on the spectral problem with the equipped local time-fractional derivative, the local tfKdV equation with Lax integrability is then derived and solved by extending the spectral transform.
As a result, a formula of exact solution with Mittag-Leffler functions is obtained.
Finally, in the case of reflectionless potential the obtained exact solution is reduced to fractional n-soliton solution.
In order to gain more insights into the fractional n-soliton dynamics, the dynamical evolutions of the reduced fractional one-, two-, and three-soliton solutions are simulated.
It is shown that the velocities of the reduced fractional one-, two-, and three-soliton solutions change with the fractional order.
American Psychological Association (APA)
Zhang, Sheng& Wei, Yuanyuan& Xu, Bo. 2019. Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example. Complexity،Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1132803
Modern Language Association (MLA)
Zhang, Sheng…[et al.]. Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example. Complexity No. 2019 (2019), pp.1-9.
https://search.emarefa.net/detail/BIM-1132803
American Medical Association (AMA)
Zhang, Sheng& Wei, Yuanyuan& Xu, Bo. Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example. Complexity. 2019. Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1132803
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132803