共查询到20条相似文献,搜索用时 93 毫秒
1.
REN Ji RUAN Hang-Yu 《理论物理通讯》2008,50(9):575-578
We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Sehroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (CLGRM), the abundant solutions of NLSE and HONLSE are obtained. 相似文献
2.
We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger (NLS) equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations. 相似文献
3.
An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented. 相似文献
4.
Alisher Yakhshimuratov 《Mathematical Physics, Analysis and Geometry》2011,14(2):153-169
In this work the method of inverse spectral problem is applied to the integration of the nonlinear Schrödinger equation with a self-consistent source in the class of periodic functions. 相似文献
5.
TANG Chen ZHANG Fang YAN Hai-Qing CHEN Zhan-Qing LUO Tao 《理论物理通讯》2005,44(3):435-439
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate. 相似文献
6.
R. Zeller R. Podloucky P. H. Dederichs 《Zeitschrift für Physik B Condensed Matter》1980,38(2):165-168
We report self-consistent calculations for the electronic and magnetic structure of 3d-impurities in Cu and Ag. Exchange and correlation effects between the electrons are treated in the local spin-density approximation, and the corresponding one-electron Schroedinger equation is solved by the Korringa-Kohn-Rostocker-Green's function method. Without adjustable parameters we obtain results for the local density of states and the magnetic moments of the impurities. 相似文献
7.
HAN Zhao-Xiu 《理论物理通讯》2007,47(1):10-14
The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication. 相似文献
8.
The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources. 相似文献
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ZHANGJin-liang WANGMing-liang FANGZong-de 《原子与分子物理学报》2004,21(1):78-82
By using the extended F-expansion method,the exact solutions,including periodic wave solutions expressed by Jaeobi elliptic functions,for (2 1)-dimensional nonlinear Schroedinger equation are derived.In the limit cases,the solitary wave solutions and the other type of traveling wave solutions for the system are obtained. 相似文献
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The propagation of dark solitons in nonlinear media that include gain and Joss described by a nonlinear Schroedinger equation is investigated. Based on the direct approach of perturbation theorv, the width, height and other related quantities of dark solitons are obtained. It is shown that stationarv propagation of dark solitons is found to be possible in the presence of both gain and absorption. The results obtained by means of our analytic method are in excellent agreement with numerical simulations. Our results are helpful for the research into the optical soliton transmission system. 相似文献
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15.
O. V. Volkov 《Physics of the Solid State》1998,40(6):1019-1027
An efficient method is proposed for the self-consistent calculation of Landau levels of a quasi-two-dimensional hole gas at
a GaAs/AlGaAs heterostructure in a perpendicular magnetic field. The method is based on transforming the Schroedinger and
Poisson equations to a system of nonlinear differential equations which are then spatially discretized and solved by the method
of relaxation. The method proposed is used to model the optical spectra for recombination of the quasi-two-dimensional hole
gas with electrons localized at a dlayer of donors in an isolated p-type heterojunction. Particular attention is paid to effects associated with the dependence of the wave functions and shape
of the potential well on the magnetic field, which have not been considered before.
Fiz. Tverd. Tela (St. Petersburg) 40, 1117–1125 (June 1998) 相似文献
16.
Oleksandr Chvartatskyi Aristophanes Dimakis Folkert Müller-Hoissen 《Letters in Mathematical Physics》2016,106(8):1139-1179
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obtain in particular matrix versions of self-consistent source extensions of the KdV, Boussinesq, sine-Gordon, nonlinear Schrödinger, KP, Davey–Stewartson, two-dimensional Toda lattice and discrete KP equation. We also recover a (2+1)-dimensional version of the Yajima–Oikawa system from a deformation of the pKP hierarchy. By construction, these systems are accompanied by a hetero binary Darboux transformation, which generates solutions of such a system from a solution of the source-free system and additionally solutions of an associated linear system and its adjoint. The essence of all this is encoded in universal equations in the framework of bidifferential calculus. 相似文献
17.
ZHANG Da-Jun WU Hua 《理论物理通讯》2008,49(4):809-814
This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate case of two solitons and "ghost" solitons, etc. Co-moving coordinate frames are employed in asymptotic analysis. 相似文献
18.
《Journal of Nonlinear Mathematical Physics》2013,20(2):323-336
A new type of the nonisospectral KP equation with self-consistent sources is constructed by using the source generation procedure. A new feature of the obtained nonisospectral system is that we allow y-dependence of the arbitrary constants in the determinantal solution for the nonisospectral KP equation. In order to further show integrability of the novel nonisospectral KP equation with self-consistent sources, we give a bilinear Bäcklund transformation. 相似文献
19.
V. K. Mel'nikov 《Communications in Mathematical Physics》1989,126(1):201-215
Solitary waves moving with nonconstant velocity are found in the nonlinear integrable system described by the Kadomtsev-Petviashvili equation with a self-consistent source. Explicit expressions are derived for the solutions describing the interaction of an arbitrary number of these waves. It is shown that in contrast with the decay and fusion of solitons, the decay and fusion of the above solitary waves are not of the resonance nature and proceed in the general case. The obtained results are relevant to some problems of hydrodynamics, solid state physics, plasma physics, etc. 相似文献