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The Fokas–Lenells equations: Bilinear approach
- Source :
- Studies in Applied Mathematics. 148:651-688
- Publication Year :
- 2021
- Publisher :
- Wiley, 2021.
-
Abstract
- In this paper, the Fokas-Lenells equations are investigated via bilinear approach. We bilinearize the unreduced Fokas-Lenells system, derive double Wronskian solutions, and then, by means of a reduction technique we obtain variety of solutions of the reduced equations. This enables us to have a full profile of solutions of the classical and nonlocal Fokas-Lenells equations. Some obtained solutions are illustrated based on asymptotic analysis. As a notable new result, we obtain solutions to the Fokas-Lenells equation, which are related to real discrete eigenvalues and not reported before in the analytic approaches. These solutions behave like (multi-)periodic waves or solitary waves with algebraic decay. In addition, we also obtain solutions to the two-dimensional massive Thirring model from those of the Fokas-Lenells equation.<br />Comment: 32 pages, 11 figures, appendixes and references updated
- Subjects :
- Asymptotic analysis
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Wronskian
Applied Mathematics
FOS: Physical sciences
Bilinear interpolation
Reduction (complexity)
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Applied mathematics
Exactly Solvable and Integrable Systems (nlin.SI)
Variety (universal algebra)
Algebraic number
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 14679590 and 00222526
- Volume :
- 148
- Database :
- OpenAIRE
- Journal :
- Studies in Applied Mathematics
- Accession number :
- edsair.doi.dedup.....2b3c2c3897ab5b94044972eff34c2718