题目：Equivalence between Wronskian- and Grammian-type solutions and asymptotic analysis of N-soliton solutions for the Gerdjikov-Ivanov equation

报告人：许韬  教授  中国石油大学（北京）

时间：3月15日 星期日 17:00-18:00    地点：逸夫楼 1537

摘要：For the Gerdjikov-Ivanov (GI) equation, we rigorously prove the equivalence between the Wronskian- and Grammian-type solutions derived from the elementary and binary Darboux transformations, respectively. The proof is finished by making complete Wronskian expansions and establishing the relations between the corresponding numerators and denominators of two determinant solutions. Meanwhile, some determinant identities are obtained as a byproduct upon comparing the coefficients of the same terms in the expansions. Furthermore, we conduct asymptotic analysis for N-soliton solutions on the zero and plane-wave backgrounds. Explicit asymptotic expressions are obtained as t goes to infinity, yielding the physical information of interacting solitons, such as amplitudes, velocities, and phase shifts before and after collisions. In particular, we derive the general parametric conditions for synchronous N-soliton collisions at arbitrary space-time points on both backgrounds. This scenario may be useful for understanding complex behavior for a large number of solitons, e.g., the generation of rogue waves via soliton collisions.

个人简介：许韬，男，教授，博士生导师。先后于北京航空航天大学和北京邮电大学获得学士和博士学位，2011年就职于中国石油大学(北京)，曾受留学基金委资助先后访问美国布法罗大学和加拿大麦克马斯特大学，担任北京数学会第13届理事会理事。主要从事可积系统、非线性波动问题以及人工智能算法研究，已在Studies in Applied Mathematics, Letters in Mathematical Physics, Physical Review E，Physica D，Proceedings A，Journal of Physics A，Journal of Mathematical Physics, EPL等SCI期刊发表第一、通讯作者论文40余篇，累计SCI他引次数达3000余次，ESI高被引论文5篇。主持国家自然科学基金项目1项、北京市自然科学基金项目2项，获河北省自然科学技术奖三等奖1项。