| Abstract: |
| This talk focuses on the applications of elliptic functions in integrable and non-integrable systems. It consists of two parts. Part I is concerned with non-integrable systems. It has been shown by Eremenko that under certain conditions the only meromorphic solutions to some non-integrable autonomous algebraic ODEs are elliptic functions or their degenerations. We will present a class of ODEs that satisfy these conditions. Also, this result will be generalized and some examples including the Falkner-Skan equation will be discussed. This work is joint with R. Conte and T. W. Ng.
Recently, rogue waves on the double-periodic background have been studied for several integrable systems. Part II of this talk is devoted to this subject. |
|