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Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy. (English) Zbl 1304.37046
Based on the stationary zero-curvature equation and the Lenard recursion equations, the authors derive the coupled modified Korteweg-de Vries (cmKdV) hierarchy associated with a \(3 \times 3\) matrix spectral problem. Resorting to the Baker-Akhiezer function and the characteristic polynomial of the Lax matrix for the cmKdV hierarchy, the authors 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.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
14H70 Relationships between algebraic curves and integrable systems
35Q53 KdV equations (Korteweg-de Vries equations)
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