搜索结果: 1-14 共查到“积分方程 systems”相关记录14条 . 查询时间(0.234 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebraic Structures from Integral Equations
积分方程 代数结构 代数分析
2023/11/29
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher-order Hamiltonian generalization evolution equations
高阶 哈密顿 广义演化方程
2023/11/13
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/11/13
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integral equations with bubble-type kernel via the method of moving spheres
运动球体 气泡型核 积分方程
2023/4/27
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A second order accurate, decoupled numerical scheme for magnetohydrodynamic equations
磁流体 动力学方程 二阶精确解 耦数值方案
2023/4/27
A temporally second-order accurate, fully discrete finite element method is proposed and analyzed for the magnetohydrodynamic (MHD) equations. A modified Crank-Nicolson method is used to discretize th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：可积深度学习
可积 深度学习 非线性科学 关系-可积系统
2023/5/5
介绍非线性科学与计算机发展关系-可积系统，探讨我们提出的可积深度学习的理论架构和发展方向。介绍我们有关可积深度学习的研究工作：基于PINN算法并对其改进，研究可积方程中的多孤子，高阶呼吸子，高阶怪波，周期背景下的高阶怪波，向量多孤子，孤子分子及其动力学行为；提出了基于守恒律的两阶段PINN算法，高维可积系统PINN算法、非局域可积系统PINN算法。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：带有内部跳跃条件的ODE特征值问题和logistic扩散方程
内部跳跃条件 ODE特征值问题 logistic扩散方程
2023/5/16
在本报告中, 我们首先介绍一个带有内部跳跃条件的二阶常微分方程特征值问题, 并将说明该特征值问题等价于一个带有 Dirac 势测度的测度微分方程特征值问题. 进而我们考虑更一般的带有 Dirac 势测度的测度微分方程特征值问题, 并且给出主特征值的存在性定理. 其次, 我们介绍带有内部跳跃条件的 logistic 扩散方程, 并且给出解的存在性定理. 此外, 我们还将讨论这些问题的生物学意义。
We review several recent results showing that small piecewise smooth perturbations of integrable systems may exhibit unstable behavior on the set of initial condition
of large measure. We also presen...
On a unified formulation of completely integrable systems
integrable systems Hamiltonian dynamics linear normal forms
2011/7/7
The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\...
Integrable deformations of Lotka-Volterra systems
Lotka-Volterra perturbations integrable systems Lie groups Poisson coalgebras Casimir functions N-dimensional
2011/7/5
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is
revisited by showing that the quadratic Poisson structure underlying its integrability structure
is ju...
Systematic method of generating new integrable systems via inverse Miura maps
modified integrable systems Lax representation (inverse) Miura transformation
2010/12/28
We provide a new natural interpretation of the Lax representation for an integrable system; that is,
Recursive Generation of Isochronous Hamiltonian Systems
Isochronous Hamiltonian Systems collective coordinate $Q$ isochronous oscillators
2010/4/2
We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscil...
One—．parameter optimal systems for the nonllnearevolutlon equation
Lie group Of symmetry optimal system adjoint representation nonlinear evolution equation
2009/10/29
The symmetry algebras of 1+ 1 dimensional nonlinear evolution equation arising from the motion of plane curve in affine geometry are systematically studied．It is found that the equation admits a seven...
Lyapunov-type Inequalities for Certain Nonlinear Systems on Time Scales
Nonlinear systems Hamiltonian systems Lyapunov - type inequality Discongugacy Generalized zero Time Scale
2010/2/25
In this study, we prove Lyapunov-type inequalities for certain nonlinear systems on an arbitrary time scale T by using elementary time scale calculus. These inequalities enable us to obtain a criterio...