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 【理學院講壇】理學院數學科學研究中心學術報告 發布時間：2020-07-13【告訴好友】　【關閉窗口】 會議時間：2020/7/17 14:00-19:00 　　騰訊會議ID：405 956 187 　　會議主題：李曉光、朱世輝教授學術講座 　　點擊鏈接入會，或添加至會議列表： 　　https://meeting.tencent.com/s/b6VhZ02VYot5 　　（一）報告人：李曉光教授 （四川師范大學） 　　報告題目：Local Dynamics Near Solitary Waves of the Supercritical generalized Zakharov-Kuznetsov (gZK) Equation 　　報告摘要：In this talk，we 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 　　報告人簡介：李曉光，四川師范大學數學科學學院教授、博士生導師。已主持國家自然科學基金面上項目、四川省杰出青年基金項目等項目。主要從事色散波動方程孤波解的穩定性研究，已在J. Differential Equations、Proc. Amer. Math. Soc. 、Differential Integral Equations等國內外專業學術刊物上發表論文20余篇。 　　（二）報告人：朱世輝 教授 （四川師范大學） 　　報告題目：Stability of standing waves for a fourth-order nonlinear Schrodinger equation with mixed dispersions  　　報告摘要：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). 　　報告人簡介：朱世輝，四川師范大學數學科學學院教授、博士生導師，四川省學術和技術帶頭人后備人選。已主持國家自然科學基金項目、四川省杰出青年基金項目等項目。主要從事非線性Schrodinger方程爆破解動力學性質研究，已在J. Differential Equations、J. Mathematical Physics、J. Dynamics and Differential Equations、Dynamics of PDE、《中國科學》等國內外專業學術刊物上發表論文20余篇, 并多次被國內外專家引用，SCI他引150余次，2篇論文入選ESI高被引。 【關閉窗口】
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