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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 101, Number 2, Pages 179–188 (Mi tmf1677)  

This article is cited in 1 scientific paper (total in 1 paper)

Numerical computations of integrals over paths on Riemann surfaces of genus N

J.-E. Lee

National Chiao Tung University
Full-text PDF (787 kB) Citations (1)
References:
Abstract: This paper is a continuation of work by Forest and Lee [1,2]. In [1,2] it was proved that the function theory of periodic soliton solutions occurs on the Riemann surfaces of genus N, where the integrals over path on play the most fundamental role. In this paper a numerical method is developed to evaluate these integrals. Precisely, the aim is to develop a computational code for integrals of the form
γf(z)dzR(z),orγf(z)R(z)dz,
where f(z) is any single-valued analytic function on the complex plane C, and R(z) is two-valued function on C of the form
R2(z)=2N+δk=1(zz0(k)),δ=0or1,
where {z0(k),1k2N+δ} are distinct complex numbers which play the role of the branch points of the Riemann surface ={(z,R(z))} of genus N1+δ. The integral path γ is continuous on . The numerical code is developed in “Mathematica” [3].
Received: 14.01.1994
English version:
Theoretical and Mathematical Physics, 1994, Volume 101, Issue 2, Pages 1281–1288
DOI: https://doi.org/10.1007/BF01018275
Bibliographic databases:
Language: Russian
Citation: J.-E. Lee, “Numerical computations of integrals over paths on Riemann surfaces of genus N”, TMF, 101:2 (1994), 179–188; Theoret. and Math. Phys., 101:2 (1994), 1281–1288
Citation in format AMSBIB
\Bibitem{Lee94}
\by J.-E.~Lee
\paper Numerical computations of integrals over paths on Riemann surfaces of genus $N$
\jour TMF
\yr 1994
\vol 101
\issue 2
\pages 179--188
\mathnet{http://mi.mathnet.ru/tmf1677}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1348384}
\zmath{https://zbmath.org/?q=an:0854.65021}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 101
\issue 2
\pages 1281--1288
\crossref{https://doi.org/10.1007/BF01018275}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994QY17400002}
Linking options:
  • https://www.mathnet.ru/eng/tmf1677
  • https://www.mathnet.ru/eng/tmf/v101/i2/p179
  • This publication is cited in the following 1 articles:
    1. Michael Trott, The Mathematica GuideBook for Numerics, 2006, 1  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:290
    Full-text PDF :97
    References:55
    First page:1
     
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