报告题目：High-order Localized Wave Solutions of  the New (3+1)-dimensional Kadomtsev-Petviashvili Equation

报告人： 贺劲松教授

工作单位： 深圳大学

报告时间：8月21日（周日）9:00-10:00

地点：实训中心1610

报告摘要：  

Constructing three-dimensional nonlinear evolution equations and exploring their exact solutions have always been important and open problems in real-world applications. The celebrated Korteweg-de Vries equation [KdV] and Kadomtsev-Petviashvili [KP] equation are typical examples of one-dimensional and two-dimensional integrable equations respectively. A natural issue is whether there are integrable analogs of these equations in three-dimensional space. In this talk, we give a positive answer. Through special reduction of an (4 + 2)-dimensional KP equation depending on four spatial dimensions and two temporal dimensions, which was introduced by Thanasis Fokas in an early paper [1], a new (3+1)-dimensional complex-valued KP equation is obtained. We show its Lax pair, smooth multi-soliton and high-order breathers by the Hirota bilinear method. Additionally, we also give the high-order rational solutions by using the long wave limit method. Local characteristics and key properties of these localized waves are discussed. Finally, a family of novel semi-rational solutions of the new (3+1)-dimensional complex-valued KP equation are also presented. This talk is based on a joint paper [2] with  Thanasis Fokas and Yulei Cao.

报告人简介：

贺劲松，教授，深圳大学高等研究院。主要研究领域是可积非线性偏微分方程（组）的数学理论及其物理应用，多次应邀到Universityof Cambridge，Universityof Oxford, University of Sheffield等大学访问和报告。负责国家科学基金6项（5项已经结题），入选教育部2008年度新世纪优秀人才支持计划（2009-2011）。在国内外SCI学术刊物上发表论文总计180篇（美国数学评论收录165篇）。贺教授的论文在Googlescholar中被引用5800次，入选2019年和2020年“中国高被引学者”，也应邀担任国际知名期刊Physica D编委（2021.11-2024.10），客座编委（2021.07-2022.04）。目前研究主要集中在怪波，已经发表大约80篇论文。