2016微分方程定性与分支理论研讨会日程安排
研讨会日程安排
报到地点：徐州市金晨假日酒店
报到时间：2016年4月15日下午1:00-8:00
报告时间：2016年4月16日上午8：30—12:00
研讨时间：2016年4月16日下午2：00—6:00
报告地点：江苏师范大学泉山校区静远楼1506报告厅
报告摘要和题目
主持人：杜增吉院长
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李继彬：浙江师范大学教授
报告题目：Exact Solutions and Bifurcations in the Invariant Manifolds for a Nonic Derivative Nonlinear Schr\{o}dinger equation.
报告摘要:Propagating modes in a class of nonic derivative nonlinear Schr\{o}dinger equations incorporating ninth order nonlinearity are investigated by the method of dynamical systems. Because the functions $\phi(\xi)$ and $\psi(\xi)$ in the solutions $A(x,t)=[\phi(\xi)+i\psi(\xi)]\exp(i(px-\Omega t)),\ (\xi=x-ct)$ satisfy a four-dimensional integral system having two first integrals (i.e., the invariants of motion). A planar dynamical system for the squared wave amplitude $\Phi=\phi^2+\psi^2$ can be derived in the invariant manifolds of the four-dimensional integrable system. By using the bifurcation theory method of dynamical systems, under different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions for this planar dynamical system can be given. Therefore, under some parameter conditions, solutions $A(x,t)$ and $\phi(\xi),\psi(\xi)$ can be solved. 36 exact explicit solutions of equation (1) are given.
韩茂安：上海师范大学大学教授
报告题目: 一阶微分方程的局部可积性
报告摘要: 本文研究一阶微分方程的可积性问题，我们证明在一次可微的条件下积分因子总是存在的。
张祥：上海交通大学教授
报告题目： Normalization and varieties of (partially) integrable differential systems报告摘要: In this talk we introduc our recent works on varieties and analytic normalizations. For local analytic differential systems defined in a neighborhood of an isolated singularity, we first study the varieties of their integrability and of partial integrability. Second, we prove the existence of analytic normalizations when these systems are either analytic integrable or partially analytic integrable.
Valery ROMANOVSKI： University of Maribor, Slovenia
报告题目:Centers and integrability in polynomials systems of ODEs
报告摘要:We discuss methods to study local integrability in polynomial systems of ODEs. A family of quintic systems having homogeneous nonlinearities and a system with degenerate infinity are considered in more details. We propose also an approach to find reversible systems within polynomial families of Lotka–Volterra systems with homogeneous nonlinearities.
储继峰：河海大学教授
报告题目:Stability of periodic solutions for a satellite model
报告摘要: We show that a satellite model admits at least two periodic solutions, one of them is stable and the other one is unstable. The proof is based on the analytical method and Poincare-Birkhoff twist theorem.
王荣年：上海师范大学教授
报告题目: Frechet空间上非线性多值发展方程的Aronszajn型正则性
报告摘要: 在非紧区间上我们考虑一类含有非自治无界算子族的非线性时滞发展包含。首先在紧区间上研究了解集的Aronszajn型正则性，即R_\delta结构，然后在Frechet空间上利用紧区间的结果和反极限方法得到了非紧区间上解集的Aronszajn型正则性刻画。最后，抽象结果被应用于非自治抛物型偏微分方程多值扰动型问题解集的Aronszajn型正则性研究。
