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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(I)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(II)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Harmonic analysis meets wave equation
谐波分析 符合 波动方程
2023/5/10
In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/4/13
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
Landau–Lifshitz–Gilbert 二维 有限时间 奇点形成
2023/4/19
Landau-Lifshitz-Gilbert equation (LLG) describes magnetization of ferromagnets. In this paper, we consider the singularity formation of LLG from R^2 to S^2. For any prescribed N distinct points q^{j} ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dispersion Analysis of CIP–FEM for Helmholtz Equation
亥姆霍兹方程 CIP-FEM 色散分析
2023/4/24
When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number k increases, known as `pollution effect' which is directly related to the phase diff...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global unique solutions for the inhomogeneous Navier-Stokes equation with only bounded density, in critical regularity spaces
临界正则性空间 界密度 非齐次 纳维-斯托克斯方程 全局唯一解
2023/4/25
Our work is to prove the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density $\rho_0$ is discontinuous and the i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a generalized Sasa-Satsuma equation (I)
广义萨氏方程 NLS类型方程 导数NLS方程
2023/5/8
The nonlinear Schrodinger (NLS)type equations are very important integrable equations. In this talk, we will give a brief review for NLS type equations including NLS equation, derivative NLS equation...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An overlapping domain decomposition splitting algorithm for stochastic NLS equation
随机NLS方程 重叠域 分解拆分 非线性薛定谔方程
2023/4/24
In this talk, we will introduce a novel overlapping domain decomposition splitting algorithm based on a Crank--Nisolson method is developed for the stochastic NLS equation driven by a multiplicative n...
Multiscale Asymptotic Expansion and Finite Element Methods For the Mixed Boundary Value Problems of Second Order Elliptic Equation in Perforated Domains
Homogenization Multiscale asymptotic expansion Elliptic equationof second order with rapidly oscillating coefficients Perforated domain
2012/8/8
In this paper, we will discuss the mixed boundary value problems for
the second order elliptic equation with rapidly oscillating coefficients in perforated
domains, and will present the higher-order...
A Second Order Finite Difference-Spectral Method for Space Fractional Diffusion Equation
A Second Order Finite Difference-Spectral Method Space Fractional Diffusion Equation
2012/8/7
A high order finite difference-spectral method is derived for solving space fractional diffusion equations, by combining the second order finite difference method in time and the spectral Galerkin met...
A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation
A Family of Exact Analytic Time Dependent Packet Solutions Nonlinear Schroedinger Equation Mathematical Physics
2012/6/19
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation
Relativistic point dynamics Einstein formula nonlinear Klein-Gordon equation Mathematical Physics
2012/6/15
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems wh...
Huygens' Principle for the Klein-Gordon equation in the de Sitter spacetime
Huygens’ Principle Klein-Gordon Equation de Sitter spacetime Higuchi Bound
2012/6/14
In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle if and only if the physical mass $m$ of the scalar field and the dimension $n$ of the sp...
Geometric numerical schemes for the KdV equation
KdV equation symplectic scheme multi-symplectic scheme solitonic gas wave turbulence
2012/5/29
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-...