Efficient method to calculate the eigenvalues of the Zakharov-Shabat system
- Resource Type
- Academic Journal
- Authors
- 崔世坤; 王振; Shikun Cui; Zhen Wang
- Source
- 中国物理B(英文版) / Chinese Physics B. 33(1):267-274
- Subject
- Zakharov-Shabat system
eigenvalue
numerical method
Chebyshev polynomials
- Language
- Chinese
- ISSN
- 1674-1056
A numerical method is proposed to calculate the eigenvalues of the Zakharov-Shabat system based on Chebyshev polynomials.A mapping in the form of tanh(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,tanh(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.