报告人：陈金兵 教授 东南大学

报告题目：Traveling periodic waves and breathers in the nonlocal derivative NLS equation

时间：2025年3月29日9:00-11:00

地点：数学楼2-3会议室

摘要：

     A nonlocal derivative NLS equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of particles. For the defocusing version of this equation, we prove that the linear stability of the nonzero constant background for decaying and periodic purterbations and the nonlinear stability for periodic purterbations. For the focusing version of this equation, we prove that the linear and nonlinear stability of the nonzero constant background under some restrictions. For both versions, we characterize the traveling periodic wave solutions by using Hirota's bilinear method, both on the zero and nonzero constant backgrounds. For each family of traveling periodic waves, we construct families of breathers which describe solitary waves moving across the stable background. A general breather solution with $N$ solitary waves propagating on the traveling periodic wave background is derived in a closed determinant form.

报告人简介：

陈金兵，东南大学数学学院教授、博导，江苏省333工程第三层次培养对象。曾先后访问洛桑联邦理工学院，德克萨斯大学大河谷分校，麦克马斯特大学，和悉尼大学数学系。主要从事可积非线性偏微分方程的有限带积分、谱稳定性、怪波理论等领域的研究，在国内外重要数学期刊已发表40余篇学术论文，如：Stud. Appl. Math.、J. Nonlinear Sci.、Nonlinearity等，并主持多项国家自然科学基金项目。

邀请人：刘小川 教授