【廿周年院庆学术报告82】 · 【和山数学论坛第369期】

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

二、报告人：贺劲松 教授

三、时  间：2023年6月1日（周四）10：00-11：00

四、地  点：闻理园A4-216

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 threedimensional 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, 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.

报告人简介：贺劲松教授，深圳大学博士生导师，主要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 University of Cambridge ，University of Oxford, University of Sheffield等大学访问和报告，负责国家自然科学基金6项， 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, 多次入选“中国高被引学者”。

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