主講人：孫春友教授/鄧圣福教授 蘭州大學(xué)/華僑大學(xué)
時(shí)間：2022年11月5日14:30
地點(diǎn)：騰訊會(huì)議 233 479 353
舉辦單位：數(shù)理學(xué)院
主講人介紹：孫春友，蘭州大學(xué)教授，博士生導(dǎo)師。1999年在云南大學(xué)數(shù)學(xué)系本科畢業(yè)，2005年在蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院獲基礎(chǔ)數(shù)學(xué)博士學(xué)位。主要從事非線(xiàn)性分析和無(wú)窮維動(dòng)力系統(tǒng)的研究，特別是無(wú)窮維動(dòng)力系統(tǒng)吸引子的存在性、維數(shù)估計(jì)、吸引速度估計(jì)、漸近正則性、有限維降維、時(shí)空復(fù)雜性等。截止目前，發(fā)表學(xué)術(shù)論文40余篇，多篇論文發(fā)表在研究領(lǐng)域的主要期刊上，如 Mathematische Annalen, Transaction Amer. Math. Soc.,SIAM J. Math. Anal., SIAM J. Applied Dynamical Systems, J. Differential Equations,Proceedings Royal Society Edinburgh, J. Evolutionary Equations, Nonlinearity等。 鄧圣福, 華僑大學(xué)教授，從事微分方程與動(dòng)力系統(tǒng)理論及其在水波問(wèn)題上的應(yīng)用。先后主持國(guó)家自然科學(xué)面上基金3項(xiàng)、教育部留學(xué)回國(guó)人員科研啟動(dòng)基金、中國(guó)博士后科學(xué)基金、福建省自然科學(xué)基金、廣東省自然科學(xué)基金。在A(yíng)rch. Rational Mech. Anal.、SIAM J. Math. Anal.、Nonlinearity、J. Differential Equations、Physica D等國(guó)際重要學(xué)術(shù)期刊上發(fā)表論文40多篇。
內(nèi)容介紹：
孫春友教授報(bào)告摘要：We will report our recent results about the existence of an inertial manifold for a 3D complex Ginzburg-Landau equation with periodic boundary conditions. This is a joint work with Dr. Anna Kostianko and professor Sergey Zelik.
鄧圣福教授報(bào)告摘要：This talk considers the existence of one- or two-hump solutions of a singularly perturbed nonlinear Schr?dinger (NLS) equation, which is the standard NLS equation with a third order perturbation. In particular, this equation appears in the field of nonlinear optics, where it is used to describe pulses in optical fibers near a zero dispersion wavelength. It has been shown formally and numerically that the perturbed NLS equation has one- or multi-hump solutions with small oscillations at infinity, called generalized one- or multi-hump solutions. The main purpose here is to provide the first rigorous proof of the existence of generalized one- or two-hump solutions of the singularly perturbed NLS equation. The several invariant properties of the equation, i.e., the translational invariance, the gauge invariance and the reversibility property, are essential to obtain enough free constants to prove the existence. The ideas and methods presented here may be applicable to show existence of generalized 2^k-hump solutions of the equation.