The application of trigonal curve to the Mikhailov–Shabat–Sokolov flows

We study the distribution of the total and ordinary ramification points of a trigonal curve over the intersection of this curve with rational curves on a rational normal scroll. We show, among other results, that these intersections may contain all the ramification points of the trigonal curve.

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The Alexander module of a trigonal curve. II

Singularities in Geometry and Topology 2011 ◽

10.2969/aspm/06610047 ◽

2019 ◽

Author(s):

Alex Degtyarev

Keyword(s):

Trigonal Curve

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Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy

Theoretical and Mathematical Physics ◽

10.1134/s0040577917010020 ◽

2017 ◽

Vol 190 (1) ◽

pp. 18-42 ◽

Cited By ~ 2

Author(s):

Xianguo Geng ◽

Xin Zeng

Keyword(s):

Trigonal Curve

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The $$\mathrm {al}$$ al function of a cyclic trigonal curve of genus three

Collectanea mathematica ◽

10.1007/s13348-015-0138-y ◽

2015 ◽

Vol 66 (3) ◽

pp. 311-349

Author(s):

Shigeki Matsutani ◽

Emma Previato

Keyword(s):

Trigonal Curve

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The coupled Sasa–Satsuma hierarchy: Trigonal curve and finite genus solutions

Analysis and Applications ◽

10.1142/s0219530516500214 ◽

2016 ◽

Vol 15 (05) ◽

pp. 667-697 ◽

Cited By ~ 4

Author(s):

Yunyun Zhai ◽

Xianguo Geng

Keyword(s):

Theta Function ◽

Asymptotic Expansions ◽

Meromorphic Functions ◽

Trigonal Curve ◽

Riemann Theta Function ◽

Function Representation ◽

Curvature Equation ◽

Zero Curvature ◽

Finite Genus

Based on the Lenard recursion equations and the stationary zero-curvature equation, we derive the coupled Sasa–Satsuma hierarchy, in which a typical number is the coupled Sasa–Satsuma equation. The properties of the associated trigonal curve and the meromorphic functions are studied, which naturally give the essential singularities and divisors of the meromorphic functions. By comparing the asymptotic expansions for the Baker–Akhiezer function and its Riemann theta function representation, we arrive at the finite genus solutions of the whole coupled Sasa–Satsuma hierarchy in terms of the Riemann theta function.

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