Title: NUMERICAL COMPUTATIONS OF INTEGRALS OVER PATHS ON RIEMANN SURFACES OF GENUS-N
Authors: LEE, JE
交大名義發表
應用數學系
National Chiao Tung University
Department of Applied Mathematics
Issue Date: 1-Nov-1994
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 R of genus N, where the integrals over paths on R 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 integral(gamma) f(z)dz/R(z), or integral(gamma) f(z)R(z)dz, where f(z) is any single-valued analytic function on the complex plane C, and R(z) is a two-valued function on C of the form GRAPHICS where {z(0)(k), 1 less than or equal to k less than or equal to 2N + delta} are distinct complex numbers which play the role of the branch points of the Riemann surface R = {(z, R(z))} of genus N - 1 + delta. The integral path gamma is continuous on R. The numerical code is developed in ''Mathematica'' 3 .
URI: http://dx.doi.org/10.1007/BF01018275
http://hdl.handle.net/11536/2278
ISSN: 0040-5779
DOI: 10.1007/BF01018275
Journal: THEORETICAL AND MATHEMATICAL PHYSICS
Volume: 101
Issue: 2
Begin Page: 1281
End Page: 1288
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  1. A1994QY17400002.pdf