报告时间： 2018年5月5号 上午9:00-11:30，下午14:30-16:00

报告地点：教四楼B415

报告人： 范恩贵教授 复旦大学

报告题目：The analytical solutions for the n-dimensional Boussinesq equations without viscosity

报告摘要：Abstract. In this paper, we construct two kinds of interesting explicit analytical solutions for n-dimensional Boussinesq equations without viscosity. The first kind is Cartesian linear analytical solutions with respect to velocity field u=(u_1,… u_n), The first n-1 velocity field (u_1,…, u_{n-1}) can be can be characterized by a linear transformation of a matrix A with respect to coordinates of spital variables; while last velocity u_n is characterized by the trace of the matrix A; The pressure p and temperature \theta are related to the well-known heat equation. The technique used here is matrix and curve integration theory to transform analytically solving the n-dimensional Boussinesq equations into algebraically constructing an appropriate matrix. The second kind is nonlinear solutions with respect to velocity field u=(u_1,…,u_n). The first n-1 velocity field (u_1,…, u_{n-1}) can be can be characterized by the classical $(n-1)$-dimensional Laplace equation; while the last velocity u_n is linear; The pressure p and temperature \theta are characterized by a generalized heat equation with variable coefficient. The technique used here is multi-dimensional

报告人简介：范恩贵，男，博士，教授。研究方向：数学物理、Riemann-Hilbert方法、正交多项式和随机矩阵。近年来，连续二届为国家973课题成员、主持国家自然科学基金、上海曙光计划、上海曙光计划跟踪课题等多项研究课题。应邀访问美国密苏里大学、密西根州立大学、德克萨斯大学、波兰华沙大学、香港大学、香港城市大学、日本京都大学等。在国外重要刊物上发表论文100余篇, 所发表论文被SCI刊源他引3000余次。2002年，获上海市曙光学者称号；2007年，获上海市自然科学二等奖； 2008年，获国际汤姆森路透卓越研究奖、上海市曙光跟踪学者称号；2016年获教育部自然科学二等奖；2016年获教育部自然科学二等奖；2017年获谷超豪数学奖。

报告人： 林机教授 浙江师范大学

报告题目：Stability and interaction of few-cycle pulses in Kerr medium

报告摘要：The different aspects of few-cycle pulse dynamics governed by the regularized short pulse equation (RSPE) are reported. It is shown that the RSPE provides an accurate description of the dynamics of the few-cycle pulse whose duration is larger than a single optical period when the few-cycle pulse's spectrum is in the medium's anomalous dispersion regime. The approximate solutions of the RSPE are constructed from the soliton solutions of the nonlinear Schr\"{o}dinger (NLS) equation. We demonstrate numerically that the stability of these few-cycle pulses strongly depend on their pulse duration. Furthermore, the interactions of the two and three few-cycle pulses are studied. When pulse parameters are suitably chosen, we show the elastic collision, inelastic collision and repulsive interaction between these multi few-cycle pulses. It is revealed that the interactions of the multi few-cycle pulses rely heavily on their pulse duration.

报告人简介：林机，女，博士，教授。1986年毕业浙江师范大学获理学士学位。2001年获中国科技大学理学博士学位。2001年-2004年上海交大物理系理论物理博士后流动站工作。国际理论物理中心(ICTP)协联成员。1996年破格晋升副教授，2001年晋升教授。浙江省高校中青年学科带头人, 浙江省“151”人才工程第二层次人才。主要从事孤子理论的高维模型可积性研究和非线性光学介质和光子晶体的光孤子理论。先后主持国家自然科学基金项目4项，省部级项目3项。已在国际国内重要刊物上发表SCI学术论文70余篇。曾获国家教委科技进步二等奖（排名第二）, 获浙江省高校优秀科研成果一、二等奖（排名第一）。

报告人： 李彪教授 宁波大学

报告题目：Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear Shrodinger equation

报告摘要：The novel generalized perturbation ( n, M )-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional nonlinear Shrodinger (NLS) equation by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N−1) - fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter ( a ) can control the wave structures of the (2 + 1)-dimensional NLS equation from the higher-order rogue waves ( a <> 0 ) into higher-order rational solitons ( a = 0) in ( x, t )-space with y = const . These results may predict the corresponding dynamical phenomena in the models of nonlinear optics and other physically relevant systems.

报告人简介：李彪，男，博士，教授。主要从事数学物理、Lie群及其在微分方程中的应用以及数学机械化等领域的研究工作。已在SCI系统发表学术论文100余篇，发表论文已被SCI他引1000多次。主持完成国家自然科学基金3项，浙江省自然科学基金2项。参与完成国家自然科学基金和省、市自然科学基金多项。现参加国家自然科学基金重点项目一项，主持国家自然科学基金面上1项。

报告人：陈勇教授 华东师范大学

报告题目：Rogue waves in the reverse time integrable nonlocal nonlinear equations

报告摘要： By using Darboux transformation method, we derive general rogue waves for these three nonlocal equations, solutions formulas are given under certain reductions of wave functions and adjoint wave fuctions. 2.More interestingly, we find a unied binary DT for this nonlocal DS syste. Thus, rogue wave solutions in nonlocal DSI and DSII equation can be expressed in a unied formula. 3. Dynamics of these rogue waves in further analyzed.For these reverse-time nonlocal equations, it is shown that general rogue waves can be bounded all space and time. More importantly, they can also develop finite-time collapsing singularities.

报告人简介：陈勇，男，博士，教授。上海市闵行区拔尖人才，卓越教授岗位。 长期从事非线性物理、可积系统、混沌理论、符号计算、大气和海洋动力学和数值计算等领域的研究工作。提出了一系列可以机械化实现非线性方程求解的方法，建立了非线性工程系统平台。发展了李群理论并成功应用于大气海洋物理模型的研究，在混沌理论中提出了一系列函数同步方法，研究了希尔伯特第十六问题的一个子问题（Lins- Melo-Pugh猜想）并取得一定进展。 已在SCI收录的国际学术期刊上发表论文260 余篇。发表论文的 SCI 他引3000余次。主持国家自然科学基金面上项目4项，参与了国家自然科学基金重点项目、973全球变化研究国家重大科学研究计划项目和国家自然科学基金创新群体。