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2019.07.05-The application of the theory of trigonal curves to the discrete coupled nonlinear Schrodinger hierarchy

学术报告

 

报告人:耿献国 教授,郑州大学数学与统计学院

 

题目:The application of the theory of trigonal curves to the discrete coupled nonlinear Schrodinger hierarchy

 

摘要:The discrete coupled nonlinear Schrodinger (DCNLS) hierarchy associated with a discrete 3×3 matrix spectral problem is derived, which are composed of the positive and negative flows. Utilizing the characteristic polynomial of Lax matrix for the DCNLS hierarchy, we introduce a trigonal curve with three infinite points and three zero points, from which we establish the associated Baker-Akhiezer function and meromorphic functions. The DCNLS equations are decomposed into a system of  Dubrovin-type ordinary differential equations. Using the theory of the trigonal curve and the properties of the three kinds of Abel differentials, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic functions, and in particular, that of solutions for the entire DCNLS hierarchy.

 

邀请人:刘青平 教授

 

时间:201975 16:00—17:00

 

地点:逸夫楼1537