报告题目：Interaction solutions to nonlinear partial differential equations via Hirota bilinearforms: one-lump-multi-stripe and one-lump-multi-soliton types

报告人：吕兴，北京交通大学数学学院教授

照片：

邀请人：张玉娟

报告时间：2023年5月21日10：00-11：00

报告地点：西大楼III区510

线上腾讯会议：284478168

报告人简介：

吕兴，北京交通大学教授、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，包括光纤通信、交通运输工程、流体力学以及数学物理等学科的非线性问题研究。累计发表SCI检索论文120余篇，发表论文他引4000余次，研究成果获得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。入选全球高被引科学家（跨领域）名单、爱思唯尔中国高被引学者名单。主持国家自然科学基金项目、重点研发计划任务课题、基本科研业务费项目等10余项。

报告摘要：

Interaction solutions between lump and soliton are analytical exact solutions to nonlinearpartial differential equations. The explicit expressions of the interaction solutions are of value foranalysis of the interacting mechanism. We analyze the one-lump multi-stripe and one-lump-multisolitonsolutions to nonlinear partial differential equations via Hirota bilinear forms. The one-lump-multi-stripe solutions are generated from the combined solution of quadratic functions andN exponential functions, while the one-lump-multi-soliton solutions from the combined solutionof quadratic functions and N hyperbolic cosine functions. Within the context of the derivation ofthe lump solution and soliton solution, necessary and sufficient conditions are presented for thetwo types of interaction solutions, respectively, based on the combined solutions to the associatedbilinear 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.

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