SOLITON INTERACTIONS FOR THE GENERALIZED (3+1)-DIMENSIONAL BOUSSINESQ EQUATION

2012 ◽  
Vol 26 (07) ◽  
pp. 1250062 ◽  
Author(s):  
XIAO-LING GAI ◽  
YI-TIAN GAO ◽  
XIN YU ◽  
ZHI-YUAN SUN
Keyword(s):  
Soliton Solution ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Propagation Process ◽  
Soliton Propagation ◽  
Soliton Interactions ◽  
Pass Through ◽  
The Moment ◽  
The One

Generalized (3+1)-dimensional Boussinesq equation is investigated in this paper. Through the dependent variable transformation and symbolic computation, the one- and two-soliton solutions are obtained. With the one-soliton solution, the coefficient effects in the soliton propagation process are investigated. Through analyzing the two-soliton solution, two kinds of two-soliton interactions are presented: (i) Two solitons merge into a bigger one whose amplitude increases but does not exceed the sum of the two at the moment of the collision; (ii) Two solitons can pass through each other, and their shapes keep unchanged with a phase shift after the separation. In addition, two kinds of analytic solutions are discussed: (i) "Amplitudes" of the two analytic solutions immediately turn to negative (positive) infinity after the "collision"; (ii) Two analytic solutions are fused into a higher peak (valley) at the moment of "collision", whose "amplitudes" change to negative (positive) infinity after the separation.

Soliton propagation in a magnetic-semiconducting medium

2016 ◽  
Vol 30 (01) ◽  
pp. 1550256
Author(s):  
Rashid Ali ◽  
H. A. Shah
Keyword(s):  
Soliton Solution ◽  
Hydrodynamic Model ◽  
Nonlinear Waves ◽  
Soliton Solutions ◽  
Infinite Medium ◽  
Soliton Propagation ◽  
Nonlinear Modes

The soliton solution for the nonlinear waves has been investigated in a composite magnetic-semiconducting medium. By using a hydrodynamic model of an infinite medium magnetized along the direction of propagation, a set of coupled nonlinear Zakharov equations has been derived. In the absence of carriers or magnetization, two extreme cases for the two independent decoupled nonlinear modes have been discussed. The propagation regions have also been numerically analyzed for the soliton solutions.

SOLITONS IN TWO-DIMENSIONAL ANTI-DE SITTER SPACE

2010 ◽  
Vol 25 (02n03) ◽  
pp. 289-299
Author(s):  
TONNIS TER VELDHUIS
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Soliton Solution ◽  
Quantum Correction ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
De Sitter ◽  
Fluctuation Spectrum ◽  
Background Space ◽  
The One

Soliton solutions in a scalar field theory defined on an AdS1+1 background space-time are investigated. An analytic soliton solution is obtained in a polynomial model, and the classical soliton mass is calculated. The fluctuation spectrum around the soliton solution is determined, and the one-loop quantum correction to the soliton mass is computed in the semi-classical approximation.

SOLITON PROPAGATION IN NONUNIFORM OPTICAL FIBERS

2003 ◽  
Vol 12 (03) ◽  
pp. 341-348 ◽  
Author(s):  
YAN XIAO ◽  
ZHIYONG XU ◽  
LU LI ◽  
ZHONGHAO LI ◽  
GUOSHENG ZHOU
Keyword(s):  
Optical Fibers ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Transmission System ◽  
Soliton Propagation ◽  
Soliton Transmission System ◽  
Soliton Transmission

In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two neighboring solitons.

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

scholarly journals Tropical limit of matrix solitons and entwining Yang–Baxter maps

2020 ◽  
Vol 110 (11) ◽  
pp. 3015-3051
Author(s):  
Aristophanes Dimakis ◽  
Folkert Müller-Hoissen
Keyword(s):  
Soliton Solution ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Baxter Equation ◽  
Kp Equation ◽  
Lattice Equation ◽  
Soliton Interactions ◽  
The Matrix ◽  
Tropical Limit ◽  
Toda Lattice Equation

Abstract We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter equation together with the Yang–Baxter map. Such maps have been called “entwining Yang–Baxter maps” in recent work. In fact, the map of polarizations obtained from a pure 2-soliton solution of a matrix KP equation, and already for the matrix KdV reduction, is not in general a Yang–Baxter map, but it is described by one of the two maps or their inverses. We clarify why the weaker version of the Yang–Baxter equation holds, by exploring the pure 3-soliton solution in the “tropical limit,” where the 3-soliton interaction decomposes into 2-soliton interactions. Here, this is elaborated for pure soliton solutions, generated via a binary Darboux transformation, of matrix generalizations of the two-dimensional Toda lattice equation, where we meet the same entwining Yang–Baxter maps as in the KP case, indicating a kind of universality.

scholarly journals The time interval between absorption and emission of light in fluorescence

1921 ◽  
Vol 99 (700) ◽  
pp. 362-371 ◽  
Keyword(s):  
High Speed ◽  
Resonance Radiation ◽  
Mercury Vapour ◽  
Time Interval ◽  
Absorption And Emission ◽  
First Case ◽  
Pass Through ◽  
The Moment ◽  
The One ◽  
Perforated Disc

The more recent theories of the absorption and emission of light, as in cases of resonance radiation and fluorescence, make the two processes quite distinct. According to Bohr the absorption of radiation of frequency corresponding to D 2 by non-luminous sodium vapour, is associated with the passage of an electron from an inner to an outer stable orbit; resonance radiation resulting when the electron returns to the original orbit. The time interval between these two processes is probably too short to be detected experimentally, for the faintness of the light makes it appear doubtful whether methods, similar to the one devised by Abraham and Lemoine, can be used in these cases. In the case of the fluorescence, or rather phosphorescence, of mercury vapour, I have succeeded in measuring the time interval, the vapour remaining non-luminous during the process of the absorption of light, and bursting into luminosity about 1/15000th of a second later. This, I believe, is the first case ever observed of a photo-luminescent body remaining dark during the period of excitation. In the study of processes of this nature two methods are available: we may give the substance a very high velocity of translation or rotation and cause it to pass through a very narrow and intense beam of light, or we may keep the substance stationary, illuminating it with flashes of very brief duration and examining it during the moment of excitation, or at definite moments later, through a perforated disc rotating at high speed (phosphoroscope). Both methods have been employed in the present work, the former being preferable in some respects.

On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

2015 ◽  
Vol 70 (5) ◽  
pp. 309-316 ◽  
Author(s):  
Da-Wei Zuo ◽  
Yi-Tian Gao ◽  
Xin Yu ◽  
Yu-Hao Sun ◽  
Long Xue
Keyword(s):  
Incompressible Fluid ◽  
Bilinear Form ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Dispersion Relations ◽  
Bell Polynomials ◽  
Nonlinear Dispersion ◽  
Lax Pairs ◽  
Soliton Propagation ◽  
Periodic Property

AbstractThe Boiti–Leon–Manna–Pempinelli (BLMP) equation is seen as a model for the incompressible fluid. In this article, a (3+1)-dimensional BLMP equation is investigated. With the aid of the Bell polynomials, bilinear form of such an equation is obtained. By virtue of the bilinear form, two kinds of soliton solutions with different nonlinear dispersion relations and another kind of analytic solutions are derived. Lax pairs and Bäcklund transformations are also constructed. Soliton propagation and interaction are analysed: (i) solitions with different nonlinear dispersion relations have different velocities and backgrounds; (ii) for another kind of analytic solutions with different nonlinear dispersion relations, the periodic property is displayed.

scholarly journals The Soliton Solutions and Long-Time Asymptotic Analysis for a General Coupled KdV Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Changhao Zhang ◽  
Guiying Chen
Keyword(s):  
Asymptotic Behavior ◽  
Soliton Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Elastic Collision ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Coupled Kdv Equation ◽  
Long Time ◽  
The One

A general coupled KdV equation, which describes the interactions of two long waves with different dispersion relation, is considered. By employing the Hirota’s bilinear method, the bilinear form is obtained, and the one-soliton solution and two-soliton solution are constructed. Moreover, the elasticity of the collision between two solitons is proved by analyzing the asymptotic behavior of the two-soliton solution. Some figures are displayed to illustrate the process of elastic collision.

The Munich conference of Minister-Presidents of German lands in 1947

2020 ◽  
Vol 2020 (10-2) ◽  
pp. 86-98
Author(s):  
Ivan Popov
Keyword(s):  
The State ◽  
State Governments ◽  
The West ◽  
Constitutional Development ◽  
The Moment ◽  
The One

The paper deals with the organization and decisions of the conference of the Minister-Presidents of German lands in Munich on June 6-7, 1947, which became the one and only meeting of the heads of the state governments of the western and eastern occupation zones before the division of Germany. The conference was the first experience of national positioning of the regional elite and clearly demonstrated that by the middle of 1947, not only between the allies, but also among German politicians, the incompatibility of perspectives of further constitutional development was existent and all the basic conditions for the division of Germany became ripe. Munich was the last significant demonstration of this disunity and the moment of the final turn towards the three-zone orientation of the West German elite.

scholarly journals Helium, [Fe/H] Abundances and the HR (Log TEFF, MBol) Diagram With Hipparcos Data of The Four Nearest Open Clusters: Hyades, Coma Berenices, The Pleiades and Praesepe

1998 ◽  
Vol 11 (1) ◽  
pp. 565-565
Author(s):  
G. Cayrel de Strobel ◽  
R. Cayrel ◽  
Y. Lebreton
Keyword(s):  
Main Sequence ◽  
Open Clusters ◽  
Main Sequence Stars ◽  
Spectroscopic Analyses ◽  
Solar Metallicity ◽  
Metal Abundances ◽  
The Mean ◽  
The Moment ◽  
The One ◽  
Best Fit

After having studied in great detail the observational HR diagram (log Teff, Mbol) composed by 40 main sequence stars of the Hyades (Perryman et al.,1997, A&A., in press), we have tried to apply the same method to the observational main sequences of the three next nearest open clusters: Coma Berenices, the Pleiades, and Praesepe. This method consists in comparing the observational main sequence of the clusters with a grid of theoretical ZAMSs. The stars composing the observational main sequences had to have reliable absolute bolometric magnitudes, coming all from individual Hipparcos parallaxes, precise bolometric corrections, effective temperatures and metal abundances from high resolution detailed spectroscopic analyses. If we assume, following the work by Fernandez et al. (1996, A&A,311,127), that the mixing-lenth parameter is solar, the position of a theoretical ZAMS, in the (log Teff, Mbol) plane, computed with given input physics, only depends on two free parameters: the He content Y by mass, and the metallicity Z by mass. If effective temperature and metallicity of the constituting stars of the 4 clusters are previously known by means of detailed analyses, one can deduce their helium abundances by means of an appropriate grid of theoretical ZAMS’s. The comparison between the empirical (log Teff, Mbol) main sequence of the Hyades and the computed ZAMS corresponding to the observed metallicity Z of the Hyades (Z= 0.0240 ± 0.0085) gives a He abundance for the Hyades, Y= 0.26 ± 0.02. Our interpretation, concerning the observational position of the main sequence of the three nearest clusters after the Hyades, is still under way and appears to be greatly more difficult than for the Hyades. For the moment we can say that: ‒ The 15 dwarfs analysed in detailed in Coma have a solar metallicity: [Fe/H] = -0.05 ± 0.06. However, their observational main sequence fit better with the Hyades ZAMS. ‒ The mean metallicity of 13 Pleiades dwarfs analysed in detail is solar. A metal deficient and He normal ZAMS would fit better. But, a warning for absorption in the Pleiades has to be recalled. ‒ The upper main sequence of Praesepe, (the more distant cluster: 180 pc) composed by 11 stars, analysed in detail, is the one which has the best fit with the Hyades ZAMS. The deduced ‘turnoff age’ of the cluster is slightly higher than that of the Hyades: 0.8 Gyr instead of 0.63 Gyr.

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