报告时间：2023年11月21日（星期二）16:00-17:00

报告地点：ZoomID：345 669 9134, Passcode:740791

报告人：Paolo Santini 教授

工作单位：意大利罗马大学

举办单位：数学学院

报告简介：Modulation instability and nonlinearity are the main causes of the appearanceof anomalous (rogue) waves (AWs) in several physical contexts. Thetheory of periodic AWs has been recently developed on the basic NonlinearSchrodinger (NLS) model in 1 + 1 dimensions, adapting thefinite gapmethod to the Cauchy problem for periodic initial perturbations of the homogeneousbackground solution of NLS. Also a perturbation theory ofAWs allowing one to study the leading order effects of small perturbationsof the NLS equation on the dynamics of AWs has been constructed. Inboth theories the solution is given, to leading order, in terms of elementaryfunctions of the initial data. These results allow one to establish the physical relevance of previously constructed analytic solutions, like the Akhmedievbreather and its generalizations, in physically sound Cauchy problems, andhave been tested in experiments influid dynamics and nonlinear optics.After summarizing the main aspects of the above theories, in this seminarwe present recent analytic results on the theory of RWs in multidimensions, concentrating on the Davey-Stewartson II equation, an integrable 2+1 dimensionalgeneralization of NLS. The results illustrated in this talk havebeen obtained in collaboration with P. Grinevich and F. Coppini.

报告人简介：

PaoloSantini,意大利罗马大学教授，长期从事可积系统理论研究，领导着罗马大学和意大利物理研究所的数学物理小组，是意大利国家终身教授评审委员会成员，多次担任著名国际学术会议的组织者和主席，是该领域的国际权威学者。罗马大学物理学院在全球享有盛誉，先后诞生过马可尼，费米和帕利希三位诺贝尔奖得主。