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

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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.

Zakharov-Shabat systemeigenvaluenumerical methodChebyshev polynomials

崔世坤、王振

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School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China

School of Mathematical Sciences,Beihang University,Beijing 100191,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaDalian Science and Technology Innovation Fund

52171251U2106225522310112022JJ12GX036

2024

10.1088/1674-1056/acd686

中国物理B(英文版)
中国物理学会和中国科学院物理研究所

中国物理B(英文版)

CSTPCDEI
影响因子：0.995
ISSN：1674-1056
年,卷(期)：2024.33(1)
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