报告时间：2025年4月24日 16:30开始
报 告 人：Maksim Pavlov 研究员（列别捷夫物理研究所，山东科技大学）
报告地点：9-305
报告题目：Isomonodromic Deformations and the Tsarev Generalized Hodograph Method
报告摘要：More than 45 years ago Vladimir Zakharov introduced the concept of "dispersionless limit" to the theory of Integrable systems. Integrable dispersive systems have plenty particular solutions, known in different applications. For instance: reflectionless potentials (multi-soliton and multi-phase solutions). However all these solutions in a dispersionless limit no longer exist! All these 45 years it was the open question: does exist a class of analytical solutions, which smoothly can be reduced to a class of corresponding solutions for a dispersionless limit? This problem is very important in the Topological Field Theory (WDVV, associativity equations), where one of most important tasks was: how to add infinitely many (in a generic case) higher order correction terms to semi-Hamiltonian hydrodynamic type systems with preservation of integrability in a dispersionless limit case? Our target is to demonstrate explicit presentation of such particular solutions, known as isomonodromic deformations. They appear in description of a gradient catastrophe known in one-component case as the Gurevich-Pitaevski Problem.
报告人简介：Maksim Pavlov, 俄罗斯列别捷夫物理研究所研究员, 山东科技大学研究员。Pavlov研究员系国际数学物理学界著名学者。博士毕业于俄罗斯科学院列别捷夫物理研究所，在国际著名数学家S. P. Novikov教授（菲尔兹奖获得者）的指导下获博士学位。主要从事可积系统的哈密顿结构、几何结构、代数几何解、流体动力学系统的可积性等方面的研究。相关成果发表在Comm. Math. Phys., IMRN, Nonlinearity, J. Nonlinear Sci., Stud. Appl. Math., Lett. Math. Phys.等国际著名杂志。
