【講座主題】變系數(shù)孤子方程的雙線性 B?cklund 變換

【講座時間】2022年11月18日  下午：15:00-16:00

【講座地點】保定校區(qū) 數(shù)理系 騰訊會議：171-980-173

【主講人】呂興教授 北京交通大學

【主講人簡介】

呂興，教授、博士生導師，美國南佛羅里達大學訪問學者，北京市青年教學名師。主要從事孤立子與非線性可積系統(tǒng)的研究，在Phys. Rev. E，J. Phys. A，J. Math. Phys.，Phys. Lett. A，Nonlinear Analysis:Real World Applications，Chaos等國際知名期刊發(fā)表論文120余篇，主持或參與國家級、省部級科研項目10項，發(fā)表科研論文120余篇，他引3000余次。2019-2021年連續(xù)三年入選全球高被引科學家，2020-2021年連續(xù)兩年入選愛思唯爾中國高被引學者。2019年獲教育部高等學?？茖W研究優(yōu)秀成果獎（自然科學）一等獎。

【報告內(nèi)容簡介】

The variable-coefficient two-dimensional Korteweg-de Vries (KdV) model is of considerable significance in describing many physical situations such as in canonical and cylindrical cases, and in the propagation of surface waves in large channels of varying width and depth with nonvanishing vorticity. Under investigation hereby is a generalized variable-coefficient two-dimensional KdV model with various external-force terms. With the extended bilinear method, this model is transformed into a variable-coefficient bilinear form, and then a B?cklund transformation is constructed in bilinear form. Via symbolic computation, the associated inverse scattering scheme is simultaneously derived on the basis of the aforementioned bilinear B?cklund transformation. Certain constraints on coefficient functions are also analyzed and finally some possible cases of the external-force terms are discussed.