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Volume 11, Issue 4
Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy

Minxin Jia, Xianguo Geng, Yunyun Zhai, Jiao Wei & Huan Liu

East Asian J. Appl. Math., 11 (2021), pp. 732-754.

Published online: 2021-08

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  • Abstract

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.

  • AMS Subject Headings

35Q51, 37K10, 35Q58, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-732, author = {Jia , MinxinGeng , XianguoZhai , YunyunWei , Jiao and Liu , Huan}, title = {Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {732--754}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/ 10.4208/eajam.090221.100421}, url = {http://global-sci.org/intro/article_detail/eajam/19370.html} }
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 -

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.

Jia , MinxinGeng , XianguoZhai , YunyunWei , Jiao and Liu , Huan. (2021). Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy. East Asian Journal on Applied Mathematics. 11 (4). 732-754. doi: 10.4208/eajam.090221.100421
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