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Sharp Criterion of Global Existence for Nonlinear Schrodinger Equation with a harmonic potential

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Acta Mathematica Sinica,English Series 2009年第4期25卷 537-544页

作者： Ji SHU Jian ZHANG Sichuan Provincial Key Laboratory of Computer Software Sichuan Normal University Chengdu 610066 P. R. China College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 P. R. China

This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up ... 详细信息

关键词： cross-constrained variational problem nonlinear Schodinger equation global existence,blow-up harmonic potential

Global Existence and Blow-up for a Dissipative Nonlinear Schrdinger Equation with harmonic potential

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维普期刊数据库

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Journal of Mathematical Research and Exposition 2007年第2期27卷 316-322页

作者：陈光淦张健蒲志林四川师范大学数学与软件科学学院四川成都610066

This paper is concerned with a dissipative nonlinear Schroedinger equation with a harmonic potential. By using some intricate inequalities and the argument of priori estimates, some behaviors of the solution are inves... 详细信息

关键词： dissipative nonlinear SchrSdinger equation harmonic potential global existence blow up.

Nonlinear Schrdinger equation with combined power-type nonlinearities and harmonic potential

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Applied Mathematics and Mechanics(English Edition) 2010年第4期31卷 521-528页

作者：徐润章徐闯 College of Science Harbin Engineering University Department of Mathematics Harbin Institute of Technology

This paper discusses a class of nonlinear SchrSdinger equations with combined power-type nonlinearities and harmonic potential. By constructing a variational problem the potential well method is applied. The structure of the potential well and the properties of the depth function are given. The invariance of some sets for the problem is shown. It is proven that, if the initial data are in the potential well or out of it, the solutions will lie in the potential well or lie out of it, respectively. By the convexity method, the sharp condition of the global well-posedness is given.

关键词： sharp criterion invariant manifold harmonic potential combined powertype nonlinearities

CONCENTRATION PHENOMENA TO THE NONLINEAR SCHRDINGER EQUATION WITH harmonic potential IN GENERAL DATA

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Annals of Differential Equations 2009年第1期25卷 39-45页

作者： Li Jingyu (School of Math. and Statistics, Northeast Normal University, Changchun 130024) Meng Lixin (School of Science, University of Science and Technology of Liaoning, Anshan 114044, Liaoning)

We analyze the blowup problems to the nonlinear Schrodinger equation with har-monic potential. This equation always models the Bose-Einstein condensation in lower dimensions. It is known that the mass of the blowup solutions from radially symmet-ric initial data can concentrate on the point of blowup. In this paper based on the refined compactness lemma, we extend the result to general data.

关键词： nonlinear Schrdinger equation harmonic potential blowup concen-tration

Photodetachment dynamics of H- ion in a harmonic potential plus a time-dependent oscillating electric field

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Photodetachment dynamics of H- ion in a harmonic potential p...

Oscillation properties of matter–wave bright solitons in harmonic potentials

2017年第九届全国青年计算物理学术会议

作者：王德华徐钦峰孔令斌 School of Physics and Optoelectronic Engineering Ludong University

The photodetachment dynamics of Hion in a harmonic potential plus an oscillating electric field has been studied using the time-dependent closed orbit *** analytical formula for calculating the photodetachment cross section of this system has been put *** is found that thephotodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength,but oscillates complicatedly when the oscillating electric field strength gets *** addition,the frequency of the harmonic potential and the oscillating electric field can also affect the photodetachment dynamics of this *** the increase of the frequency in the harmonic potential and the oscillating electric field,the number of the closed orbit for the detached electron is increased,which makes the oscillatory structure in the photodetachment cross section become much more *** research provides an intuitive understanding for the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent *** study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.

关键词： harmonic potential oscillating electric field time-dependent closed orbit theory photodetachment dynamics

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cnki会议

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Chinese Physics B 2022年第8期31卷 317-324页

作者： Shu-Wen Guan Ling-Zheng Meng Li-Chen Zhao School of Physics Northwest UniversityXi’an 710127China NSFC–SPTP Peng Huanwu Center for Fundamental Theory Xi’an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi’an 710127China

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

关键词： matter–wave bright soliton harmonic potential oscillation period

Profiles of Blow-up Solutions for the Gross-Pitaevskii Equation

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 597-606页

作者： Shi-hui Zhu Jian Zhang College of Mathematics Sichuan UniversityChengdu 610064China College of Mathematics and Software Science Sichuan Normal UniversityChengdu 610066China

This paper is concerned with the blow-up solutions of the Cauchy problem for Gross-Pitaevskii *** terms of Merle and Raphёel＇s arguments as well as Carles＇ transformation,the limiting profiles of blow-up solutions are *** addition,the nonexistence of a strong limit at the blow-up time and the existence of L2 profile outside the blow-up point for the blow-up solutions are obtained.

关键词： Gross-Pitaevskii equation blow-up solution Bose-Einstein condensate limiting profile harmonic potential

Dirac oscillator in noncommutative space

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Chinese Physics C 2014年第6期38卷 23-29页

作者： H.Hassanabadi S.S.Hosseini S.Zarrinkamar Physics Department Shahrood University Shahrood Iran P. O. Box: ***-316 Shahrood Iran Department of Basic Sciences Garmsar Branch Islamic Azad University Garmsar Iran

We study the Dirac oscillator problem in the presence of the Aharonov-Bohm effect with the harmonic potential in commutative and noncommutative spaces in S-= V and S =-V symmetry limits. We calculate exact energy levels and the corresponding eigenfunctions by the Nikiforov-Uvarov （NU） method and report the impact of the spin and the magnetic flux on the problem. Helpful numerical data is included.

关键词： Dirac oscillator Aharonov-Bohm effect harmonic potential noncommutative space Nikiforov-Uvarov(NU) method

Limiting profile of blow-up solutions for the Gross-Pitaevskii equation

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Science China Mathematics 2009年第5期52卷 1017-1030页

作者： ZHU ShiHui ZHANG Jian LI XiaoGuang College of Mathematics Sichuan UniversityChengdu 610064China College of Mathematics and Software Science Sichuan Normal UniversityChengdu 610066China College of Economics Sichuan Normal UniversityChengdu 610066China

This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limiting profile of blow-up solutions with critical mass in the corresponding weighted energy space. Moreover, we extend this result to small super-critical mass case by the variational methods and scaling technique.

关键词： Gross-Pitaevskii equation blow-up solution Bose-Einstein condensate harmonic potential concentration compact principle small super-critical mass 35B35 35Q53