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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Transport properties of Gaussian measures for nonlinear Schrodinger equations
非线性 薛定谔方程 高斯测度 输运性质
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2023/11/13
In the statistical study of Hamiltonian PDEs out of the equilibrium (lack of invariant measures), it is a natural question to understand the transport properties for canonical Gaussian measures. The f...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Normalized solutions of nonlinear Schrodinger equations with exponential critical growth
指数临界增长 非线性薛定谔方程 归一化解
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2023/5/15
In this talk, we consider normalized solutions of nonlinear Schrodinger equations in the plane when the nonlinearity satisfies an exponential critical growth. To study the normalized solutions by usin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear Schrodinger equations on metric graphs
度量图 非线性 薛定谔方程
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2023/5/12
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Improved error estimates of the splitting methods for the long-time dynamics for the weakly nonlinear Schrodinger equations
弱非线性薛定谔方程 长时间动力学 分裂方法 误差估计
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2023/4/21
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dynamics of multi-solitons to Klein-Gordon equations
多孤子 克莱因-戈登方程 动力学
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2023/4/21
I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 Schroinger equations
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2023/4/13
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 薛定谔方程
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2023/4/18
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonrelativistic limit of the Klein-Gordon equations: convergence rates and long time approximations
克莱因-戈登方程 非相对论极限 收敛率 长时间近似
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2023/4/18
We study the nonrelativistic limit of the cubic Klein-Gordon equations. We show the cubic Klein-Gordon equation converges to the cubic Schr\"odinger equation with a convergence rate of order $\epsilon...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On nonlinear Schrodinger-type equations with nonlinear damping
非线性阻尼 非线性 薛定谔型方程
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2023/4/25
In this talk，I will introduce equations of nonlinear Schrodinger-type augmented by nonlinear damping terms. The nonlinear damping can prevent finite time blow-up in several situations. The solution of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Splitting Numerical Schemes for Two-dimensional Maxwell-Debye Equations
二维 麦克斯韦-德拜方程组 拆分数值方案
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2023/4/27
In this talk, we are interested in designing some efficient numerical methods for Maxwell-Debye equations in metamaterials with negative refractive index. Dimensional splitting method is used to reduc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some results on the nonlinear logarithmic Schrodinger equations
非线性对数 薛定谔方程 量子力学
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2023/4/28
In this talk, we are concerned with the nonlinear logarithmic Schrodinger equations. When the potential satisfies a global assumption, we give the multiple solutions. When the potential satisfies a lo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The linearized Vlasov and Vlasov-Fokker-Planck equations in a uniform magnetic field
均匀磁场 线性化 Vlasov Vlasov-Foker-Planck方程
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2023/5/17
We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider periodic confinement ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Energy/dissipation-preserving split Birkhoffian multi-symplectic methods for Maxwell’s equations
麦克斯韦方程组 能量/耗散守恒分裂 Birkhofian 多辛方法
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2023/5/18
We propose a novel kind of energy/dissipation-preserving split Birkhoffian multi-symplectic (S-BMS) methods for Maxwell's equations with dissipation terms. After investigating the non-autonomous and a...
On solutions of Maxwell’s equations with dipole sources over a thin conducting film
solutions of Maxwell’s equations dipole sources conducting film
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2015/10/16
We derive and interpret solutions of time-harmonic Maxwell’s equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. Graphene sheet, lying between two unbo...
Construction of dKP and BKP Equations with Self-consistent Sources
Construction dKP BKP Equations Self-consistent Sources
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2012/8/7
A new procedure is 痳stly proposed to construct soliton equations
with self-consistent sources(SESCSs) in bilinear forms, starting from the Gram-type
determinant solution or Gram-type pfa盿n solution ...