报告人：陈金兵 教授
报告题目：Periodic waves in the Jaulent-Miodek equation: modulational stability and algebraic solitons
报告时间：2026年4月17日（周五）下午3：00
报告地点：腾讯会议：578-209-432
主办单位：数学与统计学院、数学研究院、科学技术研究院
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, 并主持多项国家自然科学基金。
报告摘要：
We study the integrable reduction for the Jaulent--Miodek (JM) equation, in which a traveling periodic wave expressed by Jacobi elliptic functions is obtained for the JM equation. Solutions of the linearized JM equation are represented as squared eigenfunctions of the Lax system, so that the stability spectrum are connected with the Lax spectrum via a characteristic polynomial. The Lax spectrum are numerically computed by using the Floquet--Bloch decomposition of periodic solutions of Lax system, while the stability spectrum are traced out via the characteristic polynomial. Since the band of stability spectrum lies on the imaginary axis, the traveling periodic wave of JM equation is proved to be modulationally stable. The Darboux transformation is retrieved in a different way, from which a new algebraic soliton is obtained at the endpoint of continuous spectral band, and three new periodic waves are derived with three discrete eigenvalues.