報(bào)告人：張玉峰 教授
報(bào)告題目：The inverse spectral method, nonlinear Fourier transforms and integrability of the high-dimensional Date Jimbo-Kashiwara-Miwa equation
報(bào)告時(shí)間：2026年1月17日（周六）上午11：20
報(bào)告地點(diǎn)：云龍校區(qū)智華樓205報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
張玉峰，中國(guó)礦業(yè)大學(xué)教授、博士生導(dǎo)師。主要研究方向?yàn)橛?jì)算力學(xué)、智能材料與結(jié)構(gòu)力學(xué)、巖石力學(xué)與工程，聚焦于多物理場(chǎng)耦合模擬、機(jī)器學(xué)習(xí)在力學(xué)中的應(yīng)用、深部地下工程穩(wěn)定性分析等。現(xiàn)任國(guó)際期刊《International Journal of Mining Science and Technology》青年編委，并擔(dān)任多個(gè)國(guó)內(nèi)外主流力學(xué)與巖土工程期刊審稿人。研究工作獲國(guó)家自然科學(xué)基金優(yōu)秀青年科學(xué)基金項(xiàng)目、面上項(xiàng)目等資助。入選國(guó)家級(jí)青年人才計(jì)劃，曾獲教育部自然科學(xué)獎(jiǎng)二等獎(jiǎng)、中國(guó)巖石力學(xué)與工程學(xué)會(huì)優(yōu)秀博士學(xué)位論文獎(jiǎng)等榮譽(yù)。
報(bào)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.