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【理学院讲坛】理学院数学科学研究中心学术报告
发布时间:2020-07-13【告诉好友】 【关闭窗口】

  会议时间:2020/7/17 14:00-19:00

  腾讯会议ID:405 956 187

  会议主题:李晓光、朱世辉教授学术讲座

  点击链接入会,或添加至会议列表:

  https://meeting.tencent.com/s/b6VhZ02VYot5

  (一)报告人:李晓光教授 (四川师范大学

  报告题目:Local Dynamics Near Solitary Waves of the Supercritical generalized Zakharov-Kuznetsov (gZK) Equation

  报告摘要:In this talkwe study the local dynamics near solitary waves of the supercritical generalized Zakharov-Kuznetsov (gZK) equation in two space dimensions. First, a trichotomy for the linearization of the super- critical gZK at solitary waves is established. Then we construct local invariant manifolds of the soliton manifold and use them to classify the local dynamics. In particular, we show that i) if an initial data is not on the co-dim 1 center- stable manifold, then the forward flow will leave a neighborhood of the soliton manifold exponentially fast; ii) solitary waves are orbitally stable on the center manifold, which implies the local uniqueness of the center manifolds.  This is a joint work with Jiayin Jin

  报告人简介:李晓光,四川师范大学数学科学学院教授、博士生导师。已主持国家自然科学基金面上项目、四川省杰出青年基金项目等项目。主要从事色散波动方程孤波解的稳定性研究,已在J. Differential Equations、Proc. Amer. Math. Soc. 、Differential Integral Equations等国内外专业学术刊物上发表论文20余篇。

  (二)报告人:朱世辉 教授 (四川师范大学

  报告题目:Stability of standing waves for a fourth-order nonlinear Schrodinger equation with mixed dispersions 

  报告摘要:In this paper, we study the standing wave solutions for a fourth-order nonlinear Schrodinger equation with mixed dispersions, modelling the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. By taking into account the role of second-order dispersion term, we prove that in the mass-subcritical regime $p\in (1,1+\frac{8}{d})$, there exist orbitally stable standing waves, when $\mu\geq 0$, or $\mu\in [-\lambda_0,0)$, for some $\lambda_0:=\lambda_0(p, \|Q_p\|_2)>0$. Moreover, in the mass-critical case $p=1+\frac{8}{d}$, we  prove that the standing waves  are orbitally stable when given $\mu\in (-\dfrac{4\|\nabla Q^*\|_2^2}{\|Q^*\|_2^2}, 0)$, and $b\in (b_*,b^*)$, for some $b^*:=\|Q^*\|_2^{\frac{8}{d}}$, $b_*:=b^*(\mu, \|Q^*\|_{H^2})\geq 0$. This shows that the sign of the second-order dispersion has crucial effect on the existence of orbitally stable standing waves for the fourth-order nonlinear Schrodinger equation with mixed dispersions. This work joint with Tingjian Luo (Guangzhou University), and Shijun Zheng (Georgia Southern University).

  报告人简介:朱世辉,四川师范大学数学科学学院教授、博士生导师,四川省学术和技术带头人后备人选。已主持国家自然科学基金项目、四川省杰出青年基金项目等项目。主要从事非线性Schrodinger方程爆破解动力学性质研究,已在J. Differential Equations、J. Mathematical Physics、J. Dynamics and Differential Equations、Dynamics of PDE、《中国科学》等国内外专业学术刊物上发表论文20余篇, 并多次被国内外专家引用,SCI他引150余次,2篇论文入选ESI高被引。

      
      
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