学术报告报告题目1：On an integrable multi-component Camassa-Holm system arising from Mobius geometry
报 告人1：康静 教授 (西北大学)
报告时间：2022年 3月 19日（星期六）下午 15:00-16:00
报告地点：腾讯会议，会议号：200-841-025
报告题目2：Integrable and Superintegrable Extensions of the Rational Calogero-Moser Model
报 告人2： 黄晴 教授 (西北大学)
报告时间：2022年 3月 19日（星期六）下午 16:00-17:00
报告地点：腾讯会议，会议号：200-841-025
报告题目3：Residual Symmetry, Backlund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System
报 告人3： 姚若侠 教授 (陕西师范大学)
报告时间：2022年 3月 26日（星期六）下午 14:00-15:00
报告地点：腾讯会议，会议号：626-142-249
报告题目4： Stability of peakons for the Camassa-Holm-type integrable systems
报 告人4： 刘小川 教授 (西安交通大学)
报告时间：2022年 3月 26日（星期六）下午 15:00-16:00
报告地点：腾讯会议，会议号：626-142-249
报告题目5： An efficient numerical method to compute the ground state of rotating dipolar Bose-Einstein Condensates
报 告人5： 唐庆粦 教授 (四川大学)
报告时间：2022年 3月 26日（星期六）下午 16:00-17:00
报告地点：腾讯会议，会议号：626-142-249
报告题目6：Classification of dark solitons via topological vector potentials
报 告人6： 赵立臣 教授 (西北大学)
报告时间：2022年 3月 26日（星期六）下午 17:00-18:00
报告地点：腾讯会议，会议号：626-142-249
邀 请人：凌黎明 教授
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数学学院
2022年3月18日
报告摘要1：In this talk, we mainly study the geometric background, integrability and peaked solutions of a (1+n)-component Camassa-Holm (CH) system and some related multi-component integrable systems. Firstly, we show this system arises from the invariant curve flows in the Mobius geometry and serves as the dual integrable counterpart of a geometrical (1+n)-component KdV system in the sense of tri-Hamiltonian duality. Moreover, we obtain an integrable two-component modified CH system using a generalized Miura transformation. Finally, we provide a necessary condition, under which the dual integrable systems can inherit the Backlund correspondence from the original ones.
报告摘要2：We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system. We introduce separation coordinates to find the general Liouville integrable system. This gives a coupling of the Calogero-Moser system with a large class of potentials, generalising the series of potentials which are separable in parabolic coordinates. Particular cases are superintegrable, including Kepler and a resonant oscillator. Meanwhile, we study the conformally flat case and generalise all the previous results to this case. By introducing symmetry algebras of the kinetic energy, we reduce the systems from 3 to 2 degrees of freedom, giving rise to many interesting systems, including both Kepler type and Henon-Heiles type potentials on a Darboux-Koenigs 
background.This is a joint work with Allan P. Fordy.
报告摘要3：Under investigation in this paper is the higher-order Broer-Kaup (HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving the initial value problems, the finite symmetry transformations are presented. However, the solution which obtained from the residual symmetry is a special group invariant solutions. In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.
报告摘要4：In this talk, I want to try to survey the existing mathematical theory concerning the nonlinear stability of peakons for the Camassa-Holm-type integrable systems. And, I will introduce the corresponding results for the multi-component case achieved recently.
报告摘要5：In this talk, we will present an efficient numerical method for computing the ground state of the rotating dipolar Bose-Einstein Condensates (BEC). The method consists two main merits: (i) efficient and accurate numerical methods will be proposed to evaluate the nonlocal dipole-dipole interaction. (ii). a nonlinear conjugate gradient method, accelerated by some well-adapted preconditioners, will be developed to compute the ground states. This work is realized in collaboration with Xavier ANTOINE (IECL, Lorraine, France), Antoine LEVITT (Inria, Paris, France) and Yong ZHANG (Tianjin University, Tianjin, China).
报告摘要6:Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.
报告人1简介：康静，西北大学数学学院教授，博士生导师。陕西省杰出青年基金获得者，曾入选陕西省高校青年杰出人才支持计划，西北大学“优秀青年学术骨干支持计划”。
报告人2简介：黄晴，西北大学数学学院教授，博士生导师。主要从事数学物理、可积系统的研究，在SIGMA、Proc. R. Soc. Lond.、J. Math. Phys.等期刊上发表多篇论文。主持国家自然科学基金青年项目与面上项目，曾获2010年陕西省科学技术奖一等奖(第三完成人)。
报告人3简介： 姚若侠，陕西师范大学教授，博士生导师，现任陕西师范大学非线性科学与符号计算实验室主任，人才工作处处长；主要从事计算复杂性与符号计算、机器证明、模式识别、孤子理论等理论研究；主持完成国家自然科学基金面上项目2项、省部级项目3项；2018年以第一完成人获陕西省科学技术奖二等奖1项，2006年以第三完成人获陕西省科学技术奖二等奖1项，博士论文获上海市研究生优秀成果奖(优博论文)。
报告人4简介： 刘小川，西安交通大学数学与统计学院教授，数学系主任，博士生导师，西安交通大学“青年拔尖人才计划”入选者。主要研究孤立子稳定性理论、非线性可积系统的几何与代数性质等，在国际数学杂志Adv. Math.、CMP、ARMA、JMPA、J. Nonlinear Sci.、Nonlinearity、JDE、SIGMA、TMP等发表多篇论文，曾获国家自然科学基金委“优青”项目、重点项目子项目等的资助。
报告人5简介：唐庆粦，四川大学数学学院教授，博士生导师。唐庆粦于2008年本科毕业于北京师范大学数学与应用数学专业；2013年博士毕业于新加坡国立大学计算数学专业。唐庆粦曾先后在新加坡国立大学、阿卜杜拉国王科技大学、维也纳大学、洛林大学以及香港中文大学等高校从事博士后研究工作，并于 2017 年 9 月加入四川大学数学学院。曾先后入选四川省、国家重要人才计划；2021年入选第十三批四川省学术技术带头人后备人选。唐庆粦的研究领域是计算数学。主要从事量子物理学中的数学模型的高效计算方法及理论分析方面的研究，研究的数学模型主要为薛定谔方程和狄拉克方程。这一方向的问题广泛来源于诸如玻色爱因斯坦凝聚态、超导超流体以及低维材料等物理领域。已在SIAM Journal on Numerical Analysis、SIAM Journal on Scientific Computing、 Journal of Computational Physics 等期刊上发表多篇论文。
报告人6简介：赵立臣，西北大学物理学院教授，博士生导师，国家优秀青年基金获得者，主要针对可积系统对非线性局域波激发机制以及它们的应用开展基础性研究工作。赵立臣先后主持国家自然科学基金项目3项，省部级项目2项。在相关方向上发表学术论文60余篇。论文得到了发展中国家科学院院士Lakshmanan、欧洲物理学会主席JM Dudley教授、美国麻省理工学院T. P. Sapsis教授等知名学者的正面引用。合作撰写21世纪理论物理及交叉学科前沿丛书----《可积模型方法及其应用》的部分章节。2016 年入选“陕西省百人计划—青年项目”，2018年获“陕西省青年科技新星”，并于 2018 年以第三完成人获“陕西省科学技术奖”（基础研究类）二等奖。