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The Homoclinic Orbits in Nonlinear SchrdingerEquation

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期 129-134页

作者： Pengcheng XU, Boling GUO and Qianshun CHANG(institute of applied{2., Chinese Academy of Sciences, beijing 100080, China)(institute of applied physics and computational{2., P.O. Box 8009, beijing100088, China)

The Persistence of Homoclinic orbits for perturbed nonlinear Schrodingerequation with five degree term under even periodic boundary conditions is *** existences of the homoclinic orbits for the truncation equation is ... 详细信息

关键词： nonlinear Schr■dinger equation geometric singular perturbation theory Melnikov’s analysis

Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 107-110页

作者： Shaomei FANG and Boling GUO Department of mathematics, Shaoguan University, Shaoguan 512.05, China Graduate School, China Academy of Engineering physics,{2. 100088, China Center for Nonlinear Studies, institute of applied physics and computational Department of mathematics Shaoguan University Shaoguan 512005 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.

关键词： unbounded domain weighted space attractor

The attractor of the stochastic generalized Ginzburg-Landau equation

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Science China mathematics 2008年第5期51卷 955-964页

作者： GUO BoLing~1 WANG GuoLian~(2.) Li DongLong~3 1 institute of applied{2. and computational mathematics,P.O.Box 8009,beijing 100088,China 2.The Graduate School of China Academy of Engineering{2.,P.O.Box 2.01,beijing 100088,China 3 Department of Information and Computer Science,Guangxi University of Technology,Liuzhou 545006,China institute of applied{2. and computational mathematics Beijing China The Graduate School of China Academy of Engineering physics Beijing China Department of Information and Computer Science Guangxi University of Technology Liuzhou China

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ... 详细信息

关键词： generalized Ginzburg-Landau equation random dynamical systems random attractor 35K05

APPROXIMATION ALGORITHM FOR MAX-BISECTION PROBLEM WITH THE POSITIVE SEMIDEFINITE RELAXATION

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Journal of computational mathematics 2003年第3期21卷 357-366页

作者： Da-chuan Xu Ji-ye Han(institute of applied{2., Academy of{2. and System Sciences, Chinese Academyof Sciences, beijing 100080, China) institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.

关键词： Approximation algorithm Max-Bisection problem Semidefinite programming Approximation ratio.

Weak Periodic Solutions of Non-Newtonian Viscous Incompressible Fluids

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 56-60页

作者： Boling GUO* and Guoguang LTN** (institute of applied{2. and computational mathematics, Be1Jing 100088, China) and Guoguang LTN (Graduate School of China Academy of Engineering{2., beijing 100088, China) + (Department of mathematics, Yunnan Univ Inst. Appl. Phys. and Compl. Math. Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Department of mathematics Yunnan University Kunming 650091 China

The existence of weak periodic solution in time of non-Newtonian fluids with a time periodic forcing is established.

关键词： periodic solution weak periodic solution bipolar fluid

Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation

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Progress in Natural Science:Materials International 2008年第3期18卷 259-266页

作者： Zhengrong Liu a, Boling Guob a School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China b institute of applied{2. and computational mathematics, beijing 100088, China School of Mathematical Sciences South China University of Technology Guangzhou 510640 China institute of applied{2. and computational mathematics Beijing 100088 China

In this paper, we consider the generalized Camassa-Holm equation ut+2.ux-uxxt+ au~2.x=2.xuxx+uuxxxUnder substitution ξ=x-ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ξ-u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.

关键词： Generalized Camassa–Holm equation Explicit solutions Periodic blow-up

Recurrence spectra of He atoms in strong external fields

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Science China(physics,Mechanics & Astronomy) 2004年第4期47卷 477-484页

作者： LIN Shenglu1, LI Hongyun1, WANG Dehua2. ZHAO Wenli1 & GAO Feng1 1. Department of physics, Shandong Normal University, Jinan 2.0014, China 2. Department of mathematics and physics, Shandong institute of Architecture and Engineering, Jinan 2.0014, China Department of physics Shandong Normal University Jinan China Department of mathematics and physics Shandong Institute of Architecture and Engineering Jinan China

By employing a model potential including the electron exchange energy, we extend the semiclassical closed orbit theory to study the multielectron atoms. Using special region-splitting consistent and iterative method, we figure out the closed orbits in the corresponding classical system and calculate the recurrence spectra of triplet helium atoms in parallel electric and magnetic fields at scaled energy ε=?0.03,n≈40,n=0. The core-scattering effects have been taken into account, which lead to more peaks in the spectra. It has also been confirmed by means of the direct comparison between the spectral portrait in such a plot and those of hydrogen case. In order to compare the theoretic results with experiment, we investigate the closed orbits and recurrence spectra of helium atoms for the similar exchange potential but applied only by single electric field at scaled energy ε=?2.7 case. The spectra are in good agreement with the experimental observation. We conclude that our model is correct and it is necessary to consider the exchange effect for determining the photoabsorption spectra of multielectron atoms in strong external fields.

关键词： exchange potential, recurrence spectra, semiclassical closed orbit theory, core-scattering.

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation

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Acta Mathematica Sinica,English Series 2002年第3期18卷 579-596页

作者： Bo Ling GUO Bi Xiang WANG institute of applied{2. and computational mathematics, P. O. Box 8009. beijing 100088. P. R. China institute of applied{2. and computational mathematics Beijing P. R. China

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.

关键词： Global solution Approximate inertial manifold Gevrey class regularity Kolmogorov-Spiegel-Sivashinsky equation

ELTA-WAVE IN A SIMPLE 1-D 2.x 2.HYPERBOLIC PROBLEM

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Journal of computational mathematics 1996年第4期14卷 311-318页

作者： S.L. Yang(institute of applied{2., Chinese Academy of Sciences, beijing, China) institute of applied{2. Chinese Academy of Sciences Beijing China

A simple one-dimensional 2.x 2.hyperbolic system is considered in the *** model contains a linear hyperbolic equation, as well as a hyperbolic equation ofwhich the coefficients are about the solution of the linear one. The exact solution ispresented and discussed, then numerical experiments are given by TVD (or MmB)type schemes for Riemann problems. From the results, we know that the solutionsdo have δ-waves for some suitable initial data.

关键词： Zhang Figure DELTA-WAVE IN A SIMPLE 1-D 2 HYPERBOLIC PROBLEM