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Algebro‐geometric constructions of the Wadati‐Konno‐Ichikawa flows and applications
Author(s) -
Li Zhu,
Geng Xianguo,
Guan Liang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3516
Subject(s) - mathematics , hierarchy , meromorphic function , recursion (computer science) , algebraic curve , type (biology) , algebraic number , pure mathematics , theta function , matrix (chemical analysis) , function (biology) , algebra over a field , mathematical analysis , algorithm , ecology , materials science , evolutionary biology , economics , market economy , composite material , biology
With the aid of Lenard recursion equations, we derive the Wadati–Konno–Ichikawa hierarchy. Based on the Lax matrix, an algebraic curveK nof arithmetic genus n is introduced, from which Dubrovin‐type equations and meromorphic function φ are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of φ and the algebro‐geometric characters ofK n . Copyright © 2015 John Wiley & Sons, Ltd.