Meromorphic solutions of complex differential equations
Dr. Chengfa Wu
Department of Mathematics, The University of Hong Kong, Hong Kong
Differential equations play important roles in modeling various phenomenons. In the first part of this talk, I will present a method due to Eremenko on the classification and construction of meromorphic solutions to certain nonlinear autonomous ordinary differential equations (ODEs). Then its applications to the Swift-Hohenberg equation and Ricci solitons will be discussed.
The second part of this talk is devoted to the study on the growth, in terms of the Nevanlinna characteristic function, of meromorphic solutions of factorizable n-th order algebraic ODEs. It is shown that for generic cases all their meromorphic solutions are elliptic functions or their degenerations. Moreover, for the second order factorizable algebraic ODEs, all (except for one case) their meromorphic solutions are found explicitly. Hence, a conjecture proposed by Hayman in 1996 is verified for these second order ODEs.
About the Speaker
Dr. Wu received his Bachelor’s degree from Harbin Institute of Technology and his PhD from the University of Hong Kong. He is currently working at the University of Hong Kong as a research assistant. His research focuses on solitons, nonlinear waves and dynamics, complex analysis, differential equations, and related topics.