【講座主題】變系數(shù)孤子方程的雙線性 B?cklund 變換

【講座時(shí)間】2022年11月18日  下午：15:00-16:00

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

【主講人】呂興教授 北京交通大學(xué)

【主講人簡(jiǎn)介】

呂興，教授、博士生導(dǎo)師，美國(guó)南佛羅里達(dá)大學(xué)訪問(wèn)學(xué)者，北京市青年教學(xué)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(guó)際知名期刊發(fā)表論文120余篇，主持或參與國(guó)家級(jí)、省部級(jí)科研項(xiàng)目10項(xiàng)，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(xué)家，2020-2021年連續(xù)兩年入選愛思唯爾中國(guó)高被引學(xué)者。2019年獲教育部高等學(xué)校科學(xué)研究?jī)?yōu)秀成果獎(jiǎng)（自然科學(xué)）一等獎(jiǎng)。

【報(bào)告內(nèi)容簡(jiǎn)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.