报告题目：Soliton molecules, multi-lumps and multi-breathers for (2+1)-dimensional nonlinear integrable equations

报告人： 任博教授

工作单位： 浙江工业大学

报告时间：1月27日（周六）16:30-17:30

地点：实训中心1710

摘要：The (2+1)-dimensional KdVSKR equation which consists of the KdV equation and the SK equation is studied. Soliton molecules of the KdVSKR equation are given by means of the velocity resonance mechanism. By selecting the values of the phases, soliton molecule bounded by the three solitons is transferred to other type of the solitonmolecule bounded by the asymmetric soliton and one soliton. Multi-breather solutions are derived by selecting the complex conjugate relations in the parameters. The relative positions for the maximum amplitudes of the multi-breathers can adjust with different values of the phases. It demonstrates that the phases of the multi-soliton solutions play an important effect in certain phenomena. In the meanwhile, the interactions between a soliton molecule and one-order breather, and between a soliton molecule and one-order lump of the KdVSKR equation are analyzed. The interactions are an elastic collisions by both the analytical and graphical ways.

报告人简介：任 博，浙江工业大学数学学院教授，博士生导师，主要从事非线性可积系统和超标准模型理论研究。已在Phys. Rev. D, Phys. Lett. B, Phys. Rev. E, J. Math. Phys., J. High Ener. Phys.等SCI收录的杂志上发表80余篇学术论文，论文总引用1000余次，其中1篇论文入选2012年中国百篇最具影响国际学术论文，1篇论文被国际知名科学/科技新闻杂志《New Scientist》刊登文章报道，2篇论文获绍兴市自然科学优秀论文一等奖。主持国家自然科学基金面上项目1项、国家自然科学基金青年项目1项和浙江省自然科学基金项目1项。入选 2019年度绍兴市优秀科技工作者先进典型，2020年度绍兴市青年科技英才。