Efficient method to calculate the eigenvalues of the Zakharov–Shabat system  

作　　者：崔世坤 王振 Shikun Cui;Zhen Wang(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China;School of Mathematical Sciences,Beihang University,Beijing 100191,China)

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]School of Mathematical Sciences,Beihang University,Beijing 100191,China

出　　处：《Chinese Physics B》2024年第1期243-249,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos.52171251,U2106225,and 52231011);Dalian Science and Technology Innovation Fund (Grant No.2022JJ12GX036)。

摘　　要：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.

关 键 词：Zakharov–Shabat system EIGENVALUE numerical method Chebyshev polynomials 

分 类 号：O241.6[理学—计算数学]