報告人：陳金兵 教授

報告題目：Periodic waves in the Jaulent-Miodek equation: modulational stability and algebraic solitons

報告時間：2026年4月17日（周五）下午3：00

報告地點：騰訊會議：578-209-432

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

陳金兵，東南大學數學學院教授、博導，江蘇省333工程第三層次培養對象。曾先后訪問洛桑聯邦理工學院，德克薩斯大學大河谷分校，麥克馬斯特大學，和悉尼大學數學系。主要從事可積非線性偏微分方程的有限帶積分、譜穩定性、怪波理論等領域的研究，在國內外重要數學期刊已發表40余篇學術論文，如：Stud. Appl. Math., J. Nonlinear Sci., Nonlinearity, 并主持多項國家自然科學基金。

報告摘要：

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.