共查询到20条相似文献,搜索用时 15 毫秒
1.
Nakatsuji H 《Physical review letters》2004,93(3):030403
We propose the scaled Schr?dinger equation and the related principles, and construct a general method of calculating the exact wave functions of atoms and molecules in analytical forms. The nuclear and electron singularity problems no longer occur. Test applications to hydrogen atom, helium atom, and hydrogen molecule are satisfactory, implying a high potentiality of the proposed method. 相似文献
2.
Exact solutions for nonlinear Schr?dinger equation in phase space: applications to Bose-Einstein condensate
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The stationary-state nonlinear Schr?dinger equation, which models the dilute-gas Bose-Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The eigenfunctions in position and momentum spaces are obtained through the ‘Fourier-like' projection transformation from the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example. 相似文献
3.
《Waves in Random and Complex Media》2013,23(1):30-41
An extended Fan sub-equation method is used to seek some new and more general traveling wave solutions of nonlinear Schrödinger equation (NLSE). The important fact of this method is to take the full advantage of clear relationship among general elliptic equation involving five parameters and other existing sub-equations involving three parameters. It is preferable to use this method to solve NLSE because this method gives us all the solutions obtained previously by the application of at least four methods (the method of using Riccati equation, or auxiliary ordinary differential equation method, or first kind elliptic equation or the generalized Riccati equation as mapping equation) in a unified manner. So it is shown that this method is concise and its applications are promising. 相似文献
4.
Periodic nonlinear Schrödinger equation and invariant measures 总被引:1,自引:1,他引:0
J. Bourgain 《Communications in Mathematical Physics》1994,166(1):1-26
In this paper we continue some investigations on the periodic NLSEiu
u
+iu
xx
+u|u|
p-2
(p6) started in [LRS]. We prove that the equation is globally wellposed for a set of data of full normalized Gibbs measrue
(after suitableL
2-truncation). The set and the measure are invariant under the flow. The proof of a similar result for the KdV and modified KdV equations is outlined. The main ingredients used are some estimates from [B1] on periodic NLS and KdV type equations. 相似文献
5.
B. F. Irgaziev A. M. Mukhamedzhanov Yu. V. Orlov 《Bulletin of the Russian Academy of Sciences: Physics》2009,73(6):773-777
A method has been developed for calculating the off-shell wave function by solving the inhomogeneous Schrödinger equation with allowance for the nuclear and Coulomb interactions. The off-shell wave function makes it possible to construct the off-shell scattering amplitude in order to solve the problems for three or more particles. An important application of the method is the Trojan Horse calculations of nuclear reactions that are important in nuclear astrophysics. Specific calculations are performed for neutron and proton scattering on the 7Be nucleus. The Woods-Saxon potential is used and the spin-orbital interaction is taken into account. 相似文献
6.
A new kind of non-polynomial nonlinearity is introduced in the nonlinear Schrödinger equation (NLSE) and the conditions are determined for which it admits solitary wave solutions. The study is done for two cases: one in which the nonlinear interaction is of the non-polynomial form and second in which cubic nonlinearity is also included along with the radical nonlinearity. Dark and bright solitary waves solutions are obtained in the respective cases. Further, later case is extended to conditions for which corresponding equation reduces to driven quadratic-cubic NLSE possessing cnoidal solutions with plane wave phase, which reduces to bright soliton for a certain parameter. 相似文献
7.
A new class of exact solutions with a singularity at finite time (collapse) is obtained for the nonlinear Schrödinger equation. 相似文献
8.
《Physics letters. A》2020,384(8):126180
We examine a fractional version of the discrete nonlinear Schrödinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor interaction to a long-range intersite coupling that decreases asymptotically as a power-law. For the linear case, we compute both, the spectrum of plane waves and the mean square displacement of an initially localized excitation in closed form, in terms of regularized hypergeometric functions, as a function of the fractional exponent. In the nonlinear case, we compute numerically the low-lying nonlinear modes of the system and their stability, as a function of the fractional exponent of the discrete laplacian. The selftrapping transition threshold of an initially localized excitation shifts to lower values as the exponent is decreased and, for a fixed exponent and zero nonlinearity, the trapped fraction remains greater than zero. 相似文献
9.
Two-dimensional accessible solitary wave families of the
generalized nonlocal nonlinear Schr?dinger equation are obtained by
utilizing superpositions of various single accessible solitary solutions.
Specific values of soliton parameters are selected as initial conditions and
the superposition of known single solitary solutions in the highly nonlocal
regime are launched into the nonlocal nonlinear medium with a Gaussian
response function, to obtain novel numerical solitary solutions of improved
stability. Our results reveal that in nonlocal media with the Gaussian
response the higher-order spatial accessible solitary families can exist in
various forms, such as asymmetric necklace, asymmetric fractional, and
symmetric multipolar necklace solitons. 相似文献
10.
11.
The extended third-order nonlinear Schrödinger equation and its solutions are studied on the basis of Galilean transformation and generalized Galilean invariance.Received: 15 September 2003, Published online: 12 July 2004PACS:
42.65.Tg Optical solitons; nonlinear guided waves - 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) 相似文献
12.
《Physica D: Nonlinear Phenomena》1988,31(1):78-102
A method of dynamic rescaling of variables is used to investigate numerically the nature of the focusing singularities of the cubic and quintic Schrödinger equations in two and three dimensions and describe their universal properties. The same method is applied to simulate the multi-focusing phenomena produced by simple models of saturating nonlinearities. 相似文献
13.
《Physics letters. A》2019,383(36):126028
The theory of bifurcations for dynamical system is employed to construct new exact solutions of the generalized nonlinear Schrödinger equation. Firstly, the generalized nonlinear Schrödinger equation was converted into ordinary differential equation system by using traveling wave transform. Then, the system's Hamiltonian, orbits phases diagrams are found. Finally, six families of solutions are constructed by integrating along difference orbits, which consist of Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions, solitary wave solutions, breaking wave solutions, and kink wave solutions. 相似文献
14.
15.
E.V. Doktorov 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):227-231
We argue that the integrable modified nonlinear Schr?dinger equation with the nonlinearity dispersion term is the true starting
point to analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary to the known assertions, solitons
of this equation are free of self-steepening and the breather formation is possible.
Received 29 September 2001 / Received in final form 25 January 2002 Published online 2 October 2002
RID="a"
ID="a"doktorov@dragon.bas-net.by 相似文献
16.
Joel L. Lebowitz Harvey A. Rose Eugene R. Speer 《Journal of statistical physics》1988,50(3-4):657-687
We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL 2 norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied. 相似文献
17.
《Physics letters. A》2014,378(5-6):577-583
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrödinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose–Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue wave solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations to the exact rogue wave solutions is also discussed. 相似文献
18.
Quantum mechanics equations for a system of the Bose particles are represented in the form of material field equations. A
nonlinear equation for the macroscopic one-particle wave function is derived. Using the Krylov–Bogolyubov–Mitropol’skii method
for equations in partial derivatives, nonlinear waves in the Bose–Einstein condensate are investigated. In the cubic approximation,
dispersion relations for waves are derived and nonlinear frequency shift is calculated in the first- and third-order approximations
for the interaction radius. 相似文献
19.
We present new type of Dark-in-the-Bright solution also called dipole soliton for the higher order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and subject to constraint relation among the parameters in optical context. This equation could be a model equation of pulse propagation beyond ultrashort range in optical communication systems. The solitary wave solution is composed of the product of bright and dark solitary waves. This type of pulse shape to be formed both the group velocity dispersion and third-order dispersion must be compensated. We also investigated the stability of the solitary wave solution under some initial perturbation on the parametric conditions. We have shown that the shape of pulse remains unchanged up to 20 normalized lengths even under some very small violation in parametric conditions. 相似文献
20.
E.O. Alt T. Csörgő B. Lörstad J. Schmidt-Sørensen 《The European Physical Journal C - Particles and Fields》2000,13(4):663-670
The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general,
based on a scattering wave function which is a solution of the n-body Coulomb Schr?dinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100%
from higher-order multi-particle Bose–Einstein correlation functions.
Received: 24 November 1999 / Published online: 17 March 2000 相似文献