搜索结果: 1-15 共查到“数学 soliton”相关记录28条 . 查询时间(0.051 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
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: 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：Bilinear approaches in soliton theory II: N-soliton solutions in (2+1)-dimensions
孤子理论 双线性方法 （2+1）维 N-孤子解
2023/5/6
The talk is about applications of bilinear approaches to N-soliton solutions in (2+1)-dimensions. The Hirota N-soliton condition will be analyzed, together with novel examples of (2+1)-dimensional sol...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bilinear approaches in soliton theory I: Hirota direct method and its applications in (1+1)-dimensions
孤子理论 双线性方法 广田直接法 （1+1）维
2023/5/6
We will talk about the Hirota direct method and its applications to soliton solutions in (1+1)-dimensions. Both known and new examples of soliton equations will be discussed, and generalized bilinear ...
Integrable vs. nonintegrable geodesic soliton behavior
Geodesic motion Solitons Hamiltonian system Pulsons
2015/6/30
We study confined solutions of certain evolutionary partial differential equations (PDE) in 1 + 1 space–time. The PDE we study are Lie–Poisson Hamiltonian systems for quadratic Hamiltonians defined on...
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.
Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers
Soliton self-frequency blue-shift hollow-core photonic crystal fibers
2011/7/7
We show theoretically that the photoionization process in a hollow-core photonic crystal fiber filled with a Raman-inactive noble gas leads to a constant acceleration of solitons in the time domain wi...
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation
KdV equation Gardner equation integrability multi-soliton stability
2011/2/25
Multi-soliton solutions of the Korteweg-de Vries equation (KdV)are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle [23]. The proof is surprisingly simple and com...
Soliton blue-shift in tapered photonic crystal fiber
Soliton blue-shift tapered photonic crystal fiber
2010/12/28
We show that solitons undergo a strong blue shift in fibers with a dispersion landscape that varies along the direction of propagation. The experiments are based on a small-core photonic crystal fiber...
Ultradiscrete Plücker Relation Specialized for Soliton Solutions
Ultradiscrete Plücker Relation Specialized Soliton Solutions
2010/12/28
We propose an ultradiscrete analogue of Pl¨ucker relation specialized for soliton solutions.
It is expressed by an ultradiscrete permanent which is obtained by ultradiscretizing the per-
manent, tha...
Geometric transformations and soliton equations
Differential Geometry (math.DG) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/11
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, toget...
q-Shock Soliton Evolution
Mathematical Physics (math-ph) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
By generating function based on the Jackson's q-exponential function and standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to standar...
Smooth soliton solutions of a new integrable equation by Qiao
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics(math-ph) Analysis of PDEs(math.AP) Pattern Formation and Solitons(nlin.PS)
2010/11/10
We find a transformation which relates a new third-order integrable nonlinear evolution equation, introduced recently by Qiao, with the well-known modified Korteweg - de Vries equation. Then we use th...