TY - JOUR
T1 - Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy
AU - Jia , Minxin
AU - Geng , Xianguo
AU - Zhai , Yunyun
AU - Wei , Jiao
AU - Liu , Huan
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 732
EP - 754
PY - 2021
DA - 2021/08
SN - 11
DO - http://doi.org/ 10.4208/eajam.090221.100421
UR - https://global-sci.org/intro/article_detail/eajam/19370.html
KW - Coupled KdV hierarchy, trigonal curve, Riemann theta function solution.
AB - <p style="text-align: justify;">Coupled Korteweg-de Vries hierarchy associated with a 3 × 3 matrix spectral
problem is derived via a stationary zero-curvature equation and Lenard recursion equations. Resorting to the characteristic polynomial of the Lax matrix for coupled Kortewegde Vries hierarchy, we introduce a trigonal curve $\mathscr{K}_g$ with three infinite points and establish the corresponding Baker-Akhiezer function and a meromorphic function on $\mathscr{K}_g$.
Coupled Korteweg-de Vries equations are decomposed into systems of ordinary differential equations of Dubrovin-type. Analytic Riemann theta function solutions are obtained
by using asymptotic expansions of the Baker-Akhiezer function and a meromorphic function and their Riemann theta function representations.</p>