共查询到20条相似文献,搜索用时 78 毫秒
1.
LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRDINGER EQUATION WITH WEAKLY DAMPED 总被引:2,自引:0,他引:2
The three-dimensional nonlinear Schrdinger equation with weakly damped that pos-sesses a global attractor are considered.The dynamical properties of the discrete dynamicalsystem which generate by a class of finite difference scheme are analysed.The existence ofglobal attractor is proved for the discrete dynamical system. 相似文献
2.
CAOQINGJIE ZHANGTIANDE K.DJIDJELI G.W.PRice E.H.TWIZELL 《高校应用数学学报(英文版)》1997,12(4):389-398
Soliton solutions of a class of generalized nonlinear evolution equations are discussed ana-lytically and numerically. This is done by using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions betweenthe solitons for the generalized nonlinear Sehrodinger equations. the characteristic behavior of thenonlinearity admintted in the system has been investigated and the soliton states of the system in thelimit when a→Oand a→∞ have been studled. The results presented show that the soliton phe-rtomenon is charaeteristics associated with the nonlinearities of the dynamical systems. 相似文献
3.
Zeng Xiaoyun Shi Bao 《Annals of Differential Equations》2005,21(3):507-513
In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions. 相似文献
4.
Qin Maochang 《Annals of Differential Equations》2006,22(4):546-550
Using the Krasnoselskii's fixed point theorem, the existence of positive periodic solutions to a class of nonlinear functional difference equations is studied in this paper. Some sufficient conditions for the existence of positive periodic solutions are presented. 相似文献
5.
Liang Ruixi Peng Jun Shen Jianhua 《Annals of Differential Equations》2006,22(4):502-510
The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures. 相似文献
6.
Zhu Huiyan 《Annals of Differential Equations》2005,21(1):99-105
We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation. 相似文献
7.
Han Zhenlai Sun Shurong Shi Bao 《Annals of Differential Equations》2005,21(4):556-561
In this paper, we study the global attractivity of solutions of higher order nonlinear difference equation xn+1=f(xn+1-1,xn+1-2,…,xn,xn-1,)n=0,1,2,…, where f is a continuous, positive, decreasing function on [0,+∞)1+1\{(0,…,0)}. We extend some known global behavior of the solutions of nonlinear higher order difference equations. 相似文献
8.
Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems. 相似文献
9.
PANZULIANG ZHENGKEJIE 《高校应用数学学报(英文版)》1997,12(2):151-154
It is shown in this paper that if parameters β1,β2 and β3 of a nonlinear Schrodinger equation with higher order dispersion terms (HNLS) satisfy the condition: 6β1-β2-2β3(1- 6β1k)= 0, k a real constant, then the fundamental soliton solutions of the HNLS equation exist. The exact soliton solutions are given and the relation between this condition and the known results inthe literature is also discussed. 相似文献
10.
FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE 总被引:1,自引:0,他引:1
袁益让 《数学物理学报(B辑英文版)》2005,25(3):427-438
Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred. 相似文献
11.
本文讨论了一类带调和势|x|2的非线性Schr(o)dinger方程解的长时间行为,证明了整体吸引子的存在性. 相似文献
12.
Xin-minXiang 《计算数学(英文版)》2004,22(1):89-100
Klein-Gordon-Schroedinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in R^n and Ω包含于R^n (n≤3) [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor AN, the upper semi-continuity on A which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for A and AN,etc. 相似文献
13.
Stabilization for a Fourth Order Nonlinear Schrödinger Equation in Domains with Moving Boundaries
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Octavio Paulo Vera Villagran 《偏微分方程(英文版)》2021,34(3):268-283
In the present paper we study the well-posedness using the Galerkin method and the stabilization considering multiplier techniques for a fourth-order nonlinear Schrödinger equation in domains with moving boundaries. We consider two situations for the stabilization: the conservative case and the dissipative case. 相似文献
14.
This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)]. 相似文献
15.
Fa-Yong Zhang & Shu-Juan Lu 《计算数学(英文版)》2001,19(4):393-406
A weakly damped Schrödinger equation possessing a global attractor are considered. The dynamical properties of a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case. 相似文献
16.
A. A. Pankov 《Functional Analysis and Its Applications》2003,37(1):75-77
We consider nonlinear magnetic Schrödinger equations under assumptions that imply the Palais–Smale condition for the corresponding functional and prove some results on the existence and multiplicity of solutions vanishing at infinity. 相似文献
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在关于非相对论分子物理中磁性粒子捕获电子的研究中,带逆平方势的非线性Schr?dinger方程起着重要的作用.我们重点关注该系统有限时间内的存在性和性态,并导出了该系统解爆破的一个显示精确门槛标准.进一步,证明了该系统径对称爆破解的集中性. 相似文献
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一类非线性Schr(o)dinger方程的守恒差分法与Fourier谱方法 总被引:1,自引:0,他引:1
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. 相似文献