线性Schrdinger方程的初边值问题(英文)

本文证明了非线性 Ｓｃｈｒｏｄｉｎｇｅｒ方程的初边值问题的 Ｈｓ－解（１＜ ｓ ≤ ２）的存在唯一性结果．     

一般非线性发展方程解的长时间行为

本文研究了一般形式的非线性发展方程Ｃａｕｃｈｙ问题的解关于时间的渐近性质．其结果覆盖并部分推广了导数非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程，Ｋｏｒｔｅｗｅｇ－ｄｅＶｒｉｅｓ方程和Ｂｅｎｊａｍｉｎ－Ｏｎｏ等方程的有关结果．     

Banach空间非线性混合单调Hammerstein型积分方程的迭代解

在Ｂａｎａｃｈ空间中，建立了“非线性混合单调型算子”不动点和最大最小耦合不动点的存在与迭代逼近定理，并应用到序Ｂａｎａｃｈ空间非线性混合单调Ｈａｍｍｅｒｓｔｅｉｎ型积分方程．     

高阶Schrodinger方程的整体强解

本文首先引入高阶Ｓｃｈｒｏｄｉｎｇｅｒ方程容许对的概念，进而给出了线性亢介Ｓｃｈｒｏｄｉｎｇｅｒ方程解的空间时估计，利用空时估计及非线性函数的估计，证明了高阶非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程整体强解的存在唯一性。     

高阶Schrodinger方程的差分格式

高阶Ｓｃｈｒｏｄｉｎｇｅｒ方程的差分格式曾文平（泉州华侨大学应用数学系泉州３６２０ｉｆ）关键词：显式差分格式；稳定性分析；高阶Ｓｃｈｒｏｄｉｎｇｅｒ方程ＡＭＳ（１９９１）主题分类：６５Ｍ０６，６５Ｍ１２．高阶Ｓｃｈｒｓｄｉｎｇｅｒ方程在量子力学、非线...     

Schrodinger算子的极大耗散扩张

本文研究Ｓｃｈｒｏｄｉｎｇｅｒ算子的极大耗散扩张，引入广义不定度规空间，得到在自然边界空间中，Ｓｃｈｒｏｄｉｎｇｅｒ算子极大耗散扩张表示形式，为进一步研究非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程无穷维动力系统的长期混沌行为作准备。     

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

Ｇｌｏｂａｌ　Ｅｘｉｓｔｅｎｃｅ　ａｎｄ　Ｌｉｆｅｓｐａｎ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｔｏ　ｔｈｅ　Ｃａｕｃｈｙ　Ｐｒｏｂｌｅｍｓ　ｆｏｒ　ｔｈｅ　Ｎｏｎｌｉｎｅａｒ　Ｓｃｈｒｏｄｉｎｇｅｒ　ＥｑｕａｔｉｏｎｓＧｌｏｂａｌＥｘｉｓｔｅｎｃｅａｎｄＬｉ...     

Schrdinger-Poisson问题的整体古典解

本文研究双Ｓｃｈｒｏｄｉｎｇｅｒ方程序列和Ｐｏｉｓｓｏｎ方程耦合的方程组的初边值问题, 利用不动点定理和嵌入定理,证明了其整体古典解的存在唯一性．     

具四维对称代数的变系数非线性Schrdinger方程的部分不变解

基于对称解的子群分类方法，得到了具四维对称代数的变系数非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程的部分不变解．     

Blow－Up and Mass Concentration of Solutions to the Cauchy Problem for Nonlinear Schrodinger Equations

Ｂｌｏｗ－ＵｐａｎｄＭａｓｓＣｏｎｃｅｎｔｒａｔｉｏｎｏｆＳｏｌｕｔｉｏｎｓｔｏ　ｔｈｅＣａｕｃｈｙＰｒｏｂｌｅｍｆｏｒＮｏｎｌｉｎｅａｒＳｃｈｒｏｄｉｎｇｅｒＥｑｕａｔｉｏｎｓ秦玉明Ｂｌｏｗ－ＵｐａｎｄＭａｓｓＣｏｎｃｅｎｔｒａｔｉｏｎｏｆＳｏｌｕ...     

On the Cauchy problem for the nonlinear Schrodinger equations including fractional dissipation with variable coefficient

This paper is devoted to the Cauchy problem for the nonlinear Schrodinger equation with time‐dependent fractional damping term. We prove the local existence result, and we study the global existence and blow‐up solutions.     

五次NLS方程全离散谱格式的大时间性态

Nonlinear Schroedinger equation arises in many physical problems. There are many works in which properties of the solution are studied. In this paper we use fully discrete Fourier spectral method to get an approximation solution of nonlinear weakly dissipative Schroedinger equation with quintic term. We give a large-time error estimate and obtain the existence of the approximate attractor A N^k.     

非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

一类非线性Schr(o)dinger方程的守恒差分法与Fourier谱方法

考察了一类带导数项的非线性Schrodinger方程的周期边值问题，提出了一种守恒的差分格式，在空间方向上采用Fourier谱方法，证明了格式的稳定性和收敛性．数值试验得到了与理论分析一致的结果．     

一类非线性Schr(o)dinger方程的整体小解

本文研究带有非线性项|u|~pu的高阶非线性Schr(?)dinger方程的Cauchy问题．对于p的某一取值范围。我们证明了此问题整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有较强的衰减估计。     

The mKdV Hierarchy With Integral Source

1 IntroductionThe nonlinear Schrodinger equation with integral source (NLSEIS) and the KdV equationwith integral source (KdVIS) were integrated by inverse scattering method in [1,2] and -methodin [3]. However, since the evolution equations for eigenfunction in Lax representation for NLSEISand KdVIS were not obtained, the determining scatterging data in [1-3] was quite complicatedand required some skill.In the present paper we discuss the new mKdV hierarchy with integral source (mKdV…     

Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrodinger Equation

It is well known that Feynman and Hibbs[1] used path integrals over Brownian paths to derive the standard(nonfractional) Schrodinger equation. Recently, Laskin[5, 6] showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known Schrodinger equation, then the path integral over Lévy trajectories leads to the fractional Schrodinger equation. Laskin[7] showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu[4] studied some physical applications of the fractional Schrodinger equation.     

非线性Schr■dinger方程的一种数值模拟方法

该文通过对非线性Schr■dinger方程增加耗散项,提出了一种新的三层线性差分格式.证明了该格式满足连续方程所具有的两个守恒量及收敛性和稳定性.通过数值例子与已知格式进行比较,结果表明该格式计算简单且具有较高精度.     

Solitons and other solutions to a new coupled nonlinear Schrodinger type equation

In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.     

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

In this article, the author studies the initial-(Dirichlet) boundary problem for a high-field version of the Schrodinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schrodinger equations on the unit cube. A global existence and uniqueness is established for a solution to this problem.