报告题目：Riemann-Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions
报 告 人：Prof. Vladimir Gerdjikov(Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria)
报告时间：2025年11月10日，15:30开始
报告地点：色情网
9号楼305报告厅
报告摘要：In this series Lectures, we propose another approach which substantially extends the classes of integrable Nonlinear evolution equations(NLEE). Its first advantage is that one can effectively use any polynomial dependence in the Lax-matrices. This requires correctly taking into account the symmetries of the RHP. We use the following steps: (1) Start with canonically normalized RHP with predefined contour G; (2) Specify the x and t dependence of the sewing function defined on G; (3) Introduce convenient parametrization for the solutions x_(x, t, l) of the RHP and formulate the Lax pair and the NLEE; (4) use Zakharov–Shabat dressing method to derive their soliton solutions. This requires correctly taking into account the symmetries of the RHP. (5) Define the resolvent of the Lax operator and use it to analyze its spectral properties.
报告人简介：Vladimir Gerdjikov教授，保加利亚科学院数学和信息科学研究所教授，博士毕业于俄罗斯圣彼得堡国立大学。 他是可积系统领域的国际著名学者，在可积系统几个方面如黎曼-希尔伯特方法，可积系统的代数结构，多分量可积系统等方面完成了系列创新性的成果， 相关成果发表在Comm. Math. Phys.,Nonlinearity, Inverse Problem， Stud. Appl. Math. 等国际著名杂志上。他主编的专著《Integrable Hamiltonian Hierarchies》被国际同行普遍引用，在可积系统有很大影响。
