East Asian J. Appl. Math., 11 (2021), pp. 732-754.
Published online: 2021-08
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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} }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.