应用数学系学术报告

--- 分析与偏微分方程讨论班(2023秋季第8讲)

Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms:

one-lump-multi-stripe and one-lump-multi-soliton types

吕 兴

(北京交通大学数学与统计学院教授)

报告时间： 13：00-14：00，2023-11-15（星期三中午）

报告地点： 沙河主E602

内容简介： Interaction solutions between lump and soliton are analytical exact solutions to nonlinear partial differential equations. The explicit expressions of the interaction solutions are of value for analysis of the interacting mechanism. We analyze the one-lump multi-stripe and one-lump-multisoliton solutions to nonlinear partial differential equations via Hirota bilinear forms. The one-lump- multi-stripe solutions are generated from the combined solution of quadratic functions and N exponential functions, while the one-lump-multi-soliton solutions from the combined solution of quadratic functions and N hyperbolic cosine functions. Within the context of the derivation of the lump solution and soliton solution, necessary and sufficient conditions are presented for the two types of interaction solutions, respectively, based on the combined solutions to the associated bilinear equations. Applications are made for a (2+1)-dimensional generalized KdV equation, the (2+1)-dimensional NNV system and the (2+1)-dimensional Ito equation.

报告人简介：吕兴，北京交通大学数学与统计学院教授、博士生导师，北京市青年教学名师。主要从事孤子与可积系统的研究，交叉学科领域非线性方程与非线性系统精确解与数值模拟，包括交通运输工程、信息与通信以及数学物理等学科领域非线性问题。发表科研论文120余篇，他引4000余次。主持国家自然科学基金项目、重点研发计划任务课题、北京市教委项目等10余项，2019-2022年连续四年入选全球高被引科学家，2020-2023年连续四年入选爱思唯尔中国高被引学者。研究成果获2018年教育部高等学校科学研究优秀成果奖（科学技术）自然科学奖一等奖。

邀请人：魏光美