|
|
Efficient method to calculate the eigenvalues of the Zakharov—Shabat system |
Shikun Cui(崔世坤)1 and Zhen Wang(王振)2,† |
1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; 2 School of Mathematical Sciences, Beihang University, Beijing 100191, China |
|
|
Abstract A numerical method is proposed to calculate the eigenvalues of the Zakharov—Shabat system based on Chebyshev polynomials. A mapping in the form of (ax) is constructed according to the asymptotic of the potential function for the Zakharov—Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, (ax) mapping, and Chebyshev nodes, the Zakharov—Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma—Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.
|
Received: 21 February 2023
Revised: 17 May 2023
Accepted manuscript online: 18 May 2023
|
PACS:
|
02.30.Ik
|
(Integrable systems)
|
|
02.30.Rz
|
(Integral equations)
|
|
02.70.Jn
|
(Collocation methods)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 52171251, U2106225, and 52231011) and Dalian Science and Technology Innovation Fund (Grant No. 2022JJ12GX036). |
Corresponding Authors:
Zhen Wang
E-mail: wangzmath@163.com
|
Cite this article:
Shikun Cui(崔世坤) and Zhen Wang(王振) Efficient method to calculate the eigenvalues of the Zakharov—Shabat system 2024 Chin. Phys. B 33 010201
|
[1] Manakov S V 1973 Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 65 505 [2] Zakharov V E 1972 Sov. Phys. JETP 35 908 [3] Yang X Y, Zhang Z and Li B 2020 Chin. Phys. B 29 100501 [4] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202 [5] Gardner C S, Greene J M, Kruskal M D and Miura R M 2008 Bull. Amer. Math. Soc. 46 1 [8] Boffetta G and Osborne A 1992 J. Comput. Phys. 102 252 [9] Bronski J C 1996 Physica D 97 376 [10] Burtsev S, Camassa R and Timofeyev I 1998 J. Comput. Phys. 147 166 [11] Deconinck B and Kutz J N 2006 J. Comput. Phys. 219 296 [12] Medvedev S, Vaseva I, Chekhovskoy I and Fedoruk M 2019 Opt. Lett. 44 2264 [13] Vasylchenkova A, Prilepsky J E, Shepelsky D and Chattopadhyay A. 2019 Commun. Nonlinear Sci. Numer. Simul. 68 347 [14] Yousefi M I and Kschischang F R 2014 IEEE Trans. Inf. Theory 60 4329 [15] Sezer M and Kaynak M 1996 Int. J. Math. Educ. Sci. Technol. 27 607 [16] Parlett B N 2000 Comput. Sci. Eng. 2 38 [17] Satsuma J and Yajima N 1974 Prog. Theor. Phys. 55 284 [18] Bai D and Wang J 2012 Commun. Nonlinear Sci. Numer. Simul 17 1201 [19] Yang J K 2010 Nonlinear waves in integrable and nonintegrable systems (Society for Industrial and Applied Mathematics) pp. 45-50 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|