In the paper, we want to derive a few of nonlinear Schrodinger equations with various formats and investigate their properties, such as symmetries, single soliton solutions, multi-soliton solutions, and so on. First of all, we propose an efficient and straightforward scheme for generating nonisospectral integrable hierarchies of evolution equations for which a generalized nonisospectral integrable Schrodinger hierarchy (briefly GNISH) singles out, from which we get a derivative nonlinear Schrodinger equation, a generalized nonlocal Schrodinger integrable system and furthermore we investigate the symmetries and conserved qualities of the GNISH. Next, we apply the dbar method to obtain a generalized nonlinear Schrodinger-Maxwell- Bloch (GNLS-MB) equation and its hierarchy by introducing a generalized Zakhrov-Shabat spectral problem, whose soliton solutions and gauge transformations are obtained.
会议网址:https://meeting.tencent.com/s/c0q16ItH22li
会议ID:997 927 443
会议密码:0717
张玉峰,中国矿业大学数学学院教授,博士生导师。中国科学院和郑州大学博士后。主要研究领域为数学物理中的数学符号计算、可积系统、李群分析理论,以及数学教育中的数学方法论,在Journal of Mathematical Physics、Journal of Physics A、Journal of Differential Equations等国内外学术期刊上发表学术论文100余篇,合作专著三部,入选爱思唯尔数学领域中国高被引学者。主持国家自然科学基金面上项目2项、及博士后基金项目1项。