報(bào) 告 人：張翼 教授 

報(bào)告題目：The application of bidifferential calculus in integrable systems

報(bào)告時(shí)間：2023年11月16日（周四）下午4:30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)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：

       張翼，浙江師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師，浙江師范大學(xué)動(dòng)力系統(tǒng)與非線性科學(xué)研究中心主任。浙江省應(yīng)用數(shù)學(xué)研究會(huì)副監(jiān)事長(zhǎng)；中國(guó)優(yōu)選法統(tǒng)籌法與經(jīng)濟(jì)數(shù)學(xué)研究會(huì)理事；國(guó)家科學(xué)技術(shù)獎(jiǎng)自然科學(xué)獎(jiǎng)以及多個(gè)省市自然科學(xué)獎(jiǎng)評(píng)審專家；科技部數(shù)學(xué)專項(xiàng)、教育部學(xué)位中心評(píng)審專家。主要研究方向?yàn)楣铝⒆永碚撆c可積系統(tǒng)。曾在美國(guó)南佛羅里達(dá)大學(xué)、阿拉巴馬大學(xué)、香港中文大學(xué)、日本九州大學(xué)等多所大學(xué)訪問。主持過多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目及浙江省自然科學(xué)基金研究項(xiàng)目；獲得過浙江省科學(xué)技術(shù)進(jìn)步獎(jiǎng)一等獎(jiǎng)和浙江省人民政府優(yōu)秀教學(xué)成果二等獎(jiǎng)。在SCI 源刊雜志上發(fā)表論文150余篇。

報(bào)告摘要：

       In this talk, in the framework of bidifferential calculus, we investigate the Manakov system via a matrix version of the binary Darboux transformation which involves a Lyapunov equation. With a spectral matrix of the form of diagonal and vanishing seed solutions, the corresponding matrix solution of the Lyapunov equation is given, which can contain zero entries, which should be helpful for further explorations of the solutions of equations with this method. From vanishing and nonvanishing seed solutions, abundant soliton solutions are provided corresponding to a spectral matrix of the form of a Jordan block. In particular, based on the properties of nilpotent matrices, we construct the semirational rogue wave solutions, which can demonstrate the coexistence of rational rogue wave and bright/dark soliton.