Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy

作者：Geng, Xianguo; Zhai, Yunyun^*; Dai, H. H.

来源：Advances in Mathematics, 2014, 263: 123-153.

DOI：10.1016/j.aim.2014.06.013

• cmKdV hierarchy
• Algebro-geometric solutions
• Baker-Akhiezer function
• Trigonal curve

Based on the stationary zero-curvature equation and the Lenard recursion equations, we derive the coupled modified Korteweg-de Vries (cmKdV) hierarchy associated with a 3 x 3 matrix spectral problem. Resorting to. the Baker-Akhiezer function and the characteristic polynomial of Lax matrix for the cmKdV hierarchy, we introduce a trigonal curve with three infinite points and two algebraic functions carrying the data of the divisor. The asymptotic properties of the Baker-Akhiezer function and the two algebraic functions are studied near three infinite points on the trigonal curve. Algebro-geometric solutions of the cmKdV hierarchy are obtained in terms of the Riemann theta function.

• 出版日期2014-10-1
• 单位郑州大学