报告人：张玉峰 教授
报告题目：The inverse spectral method, nonlinear Fourier transforms and integrability of the high-dimensional Date Jimbo-Kashiwara-Miwa equation
报告时间：2026年1月17日（周六）上午11：20
报告地点：云龙校区智华楼205报告厅
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：
张玉峰，中国矿业大学教授、博士生导师。主要研究方向为计算力学、智能材料与结构力学、岩石力学与工程，聚焦于多物理场耦合模拟、机器学习在力学中的应用、深部地下工程稳定性分析等。现任国际期刊《International Journal of Mining Science and Technology》青年编委，并担任多个国内外主流力学与岩土工程期刊审稿人。研究工作获国家自然科学基金优秀青年科学基金项目、面上项目等资助。入选国家级青年人才计划，曾获教育部自然科学奖二等奖、中国岩石力学与工程学会优秀博士学位论文奖等荣誉。
报告摘要：
The paper is organized in three parts: (a) We construct the Lax pair of the matrix form of the 2+1-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation, so that a nonlinear Fourier transform of the Cauchy solution u is obtained, denoted by H. The associated time evolution of u is derived by the time evolution of the nonlinear Fourier data. (b) The complexication of the independent variables x, y, t of the 2+1-dimensional DJKM equation generate the 4+2 integrable extension of the DJKM equation, we derive a nonlinear Fourier transform pair in four dimensions, which can be used for the solution of the Cauchy initial value problem of the DJKM equation in 4+2. (c) Reducing the equation from 4+2 to the 3+1 and 3+2 dimensions by transforming two time variables, and the Lax pairs of the reduced equations are given. Finally, the three dimensional Fourier transform pair and solution of the Cauchy problem for the DJKM equation in three spatial and two temporal dimensions is constructed by introducing several new long derivative operators Dx, Dy, and Dt.
