理学院:线上学术报告:Orbital stability of standing waves for the bi-harmonic nonlinear Schrödinger equation with mixed dispersions

发布者:综合科发布时间:2020-08-27浏览次数:10

报告题目:Orbital stability of standing waves for the bi-harmonic nonlinear Schrödinger equation with mixed dispersions

报告人:朱世辉教授(四川师范大学)

报告时间:20208311400-1500

腾讯会议号:344116494,密码:0831

报告摘要:

In this paper, we study the standing wave solutions for the  bi-harmonic nonlinear Schrödinger equation with a Laplacian term (BNLS),  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 for BNLS, 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 for the  BNLS are orbital 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 BNLS 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2项,教育部博士点基金项目,四川省杰出青年基金,并且获得四川省科技进步二等奖和四川优秀教师成果奖二等奖。此外,他同时是数学SCI杂志编委。朱世辉主要从事非线性Schrödinger方程爆破解动力学性质研究,已在著名数学期刊 J. Differential EquationsJ. Dynamics and Differential Equations等发表论文35,被很多国际著名学者引用,引用次数超到180次。此外,他有 2篇论文入选ESI高被引。他的工作受到国内外同行的广泛关注。