Periodic waves in the discrete mKdV equation: modulational instability and rogue waves
数学公众报告(120周年校庆系列第88场)
报告题目(Title)：Periodic waves in the discrete mKdV equation: modulational instability and rogue waves
报告人(Speaker)：陈金兵 教授(东南大学数学学院)
地点(Place)：腾讯会议ID：453 850 0147
时间(Time)：2023年4月7日(周五), 14:00-15:00
邀请人(Inviter)：王灯山
报告摘要
We derive the traveling periodic waves of the discrete modified Korteweg-de Vries equation by using the nonlinearization of Lax pair. Modulational stability of the traveling periodic waves is studied from the squared eigenfunction relation and the Lax spectrum. We use numerical approximations to show that, similar to the continuous counterpart, the family of dnoidal solutions is modulationally stable and the family of cnoidal solutions is modulationally unstable. Consequently, algebraic solitons propagate on the dnoidal wave background and rogue waves (spatially and temporally localized events) are dynamically generated on the cnoidal wave background.
主讲人简介
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，和麦克马斯特大学数学系。长期从事可积非线性偏微分方程的有限带积分、谱稳定性、非线性海洋波理论及相关领域的研究，在该领域以第一或通讯作者已发表40余篇SCI学术论文，如：Stud. Appl. Math., Rev. Math. Phys., J. Nonlinear Sci., Nonlinearity, Physica D, Phys. Rev. E等国内外重要数学期刊，并主持三项国家自然科学基金。
