報告人：張玉峰 教授

報告題目：The inverse spectral method, nonlinear Fourier transforms and integrability of the high-dimensional Date Jimbo-Kashiwara-Miwa equation

報告時間：2026年1月17日（周六）上午11：20

報告地點：云龍校區智華樓205報告廳

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：

張玉峰，中國礦業大學教授、博士生導師。主要研究方向為計算力學、智能材料與結構力學、巖石力學與工程，聚焦于多物理場耦合模擬、機器學習在力學中的應用、深部地下工程穩定性分析等。現任國際期刊《International Journal of Mining Science and Technology》青年編委，并擔任多個國內外主流力學與巖土工程期刊審稿人。研究工作獲國家自然科學基金優秀青年科學基金項目、面上項目等資助。入選國家級青年人才計劃，曾獲教育部自然科學獎二等獎、中國巖石力學與工程學會優秀博士學位論文獎等榮譽。

報告摘要：

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.