Finite-gap integration of the SU(2) Bogomolny equations

Singular spectral curves in finite gap integration

We expose some applications of the finite gap integration method which involve singular spectral curves. They include orthogonal curvilinear coordinate systems corresponding to spectral curves with geometrical genus zero, finite gap Frobenius manifolds, and soliton deformations of spectral curves corresponding to equations with self-consistent sources. This is an extended version of the talk given at the conference "Geometry, Dynamics, Integrable Systems --- GDIS 2010" (Serbia, September 7--13, 2010).

Towards Finite-Gap Integration of the Inozemtsev Model

The Inozemtsev model is considered to be a multivaluable generalization of Heun's equation. We review results on Heun's equation, the elliptic Calogero-Moser-Sutherland model and the Inozemtsev model, and discuss some approaches to the finite-gap integration for multivariable models.

Boussinesq 方程族的代数几何积分

Algebro-geometric integration of the Boussinesq hierarchy

本研究采用Holod-Flashka-Newell-Ratiu李代数方法构建Boussinesq方程的可积方程族，推导其有限隙哈密顿系统的谱曲线性质，通过多周期函数求解雅可比反演问题，得到显式精确有限隙解并给出实性条件猜想，完成了数值计算与图形展示。