Elliptic solitons and Heun's equation
A. O. Smirnov
Abstract
We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's polynomials is studied. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Monodromy group is considered. Numerous examples are given.
Create a lesson
Related papers
An equivalence principle for martingales
Grigori A. Karagulyan, Linda A. Khachatryan, Khazhakanush V. Navoyan
Macroscopic return-time spectra and Hausdorff dimension transitions
Jinjun Li
Homogeneous Polynomial Carleson Operators Along the Paraboloid
Alina Zhu
Stein's generalized spherical maximal operator
Luz Roncal
Arithmetic product theorems on self-similar sets of uniqueness and homogeneous Moran sets
Yan-Song Fu, Xu-Guang Wang, Meng Zhu
Sampling Density for Multi-window STFT Phase Retrieval
Wenchang Sun, Mengxuan Zhou