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

Xianguo Geng; Yunyun Zhai; H. H. Dai

doi:10.1016/j.aim.2014.06.013

Author(s)

Xianguo Geng
Yunyun Zhai
H. H. Dai

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	123-153
Journal / Publication	Advances in Mathematics
Volume	263
Online published	7 Jul 2014
Publication status	Published - 1 Oct 2014

Link(s)

DOI	DOI https://doi.org/10.1016/j.aim.2014.06.013 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84904015662&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(4d34bf2d-d798-4f3b-b3bd-968c3f3de86f).html

Abstract

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 × 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. © 2014 .