搜索结果: 1-15 共查到“数学 NLS”相关记录24条 . 查询时间(0.063 秒)
In this paper, we investigate the new two-Lévy-index fractional nonlinear Schr？dinger (FNLS) equations with optical lattices, where two fractional derivative terms are introduced to control the diffra...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost sure scattering for the cubic NLS on R3T1
R3T1 三次NLS 散射 Cauchy问题
2023/5/18
We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering resul...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part II discrete case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part I continuous case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Painleve asymptotics in transition region
非零背景 散焦NLS方程 过渡区 疼痛渐近
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar steepest descent method and double scaling limit, we obtain Painleve asymptotics in two transitio...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Soliton resolution in soliton region
非零背景 散焦NLS方程 孤子区域 孤子分辨率
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar generalization of the nonlinear steepest descent method to compute the leading order approximatio...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On scattering for NLS on waveguide manifolds（III）
NLS 波导流形 散射
2023/5/16
In these series talks, we will give an overview for a direction of NLS results: long time behavior for NLS on waveguide manifolds (semiperiodic spaces). We will discuss the main ideas, main tools to h...
Local Dynamics Near Unstable Branches of NLS Solitons
Local Dynamics Unstable Branches of NLS Solitons Analysis of PDEs
2012/7/11
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, so...
Soliton dynamics of NLS with singular potentials
Nonlinear Schrodinger equation soliton dynamics singular potentials
2012/6/30
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the...
The semiclassical limit of focusing NLS for a family of non-analytic initial data
semiclassical limit non-analytic initial data NLS
2011/7/7
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales....
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential
Nonlinear Schr¨odinger equation Nash-Moser Theory
2011/1/19
We prove the existence of quasi-periodic solutions for Schr¨odinger equations with a multiplicative potential on Td, d ≥ 1, merely differentiable nonlinearities, and tangential frequencies constrained...
Energy and local energy bounds for the 1-D cubic NLS equation in H^{-1/4}
Energy local energy bounds 1-D cubic NLS equation
2011/1/17
We consider the cubic Nonlinear Schr¨odinger Equation (NLS) in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time Hs bounds in terms of the ...
Dispersive estimates and NLS on product manifolds
decay estimates dispersive equations hyperbolic space
2011/1/17
We prove a general dispersive estimate for a Schr¨odinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates....
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions
Global well-posedness scattering the defocusing cubic NLS
2010/11/11
In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. ...