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well as single- and double-breather solutions of the discrete sine-Gordon equation. The dynamical features of discrete kinks and breathers are also illustrated.

The main motivation of our study is to test the ideas Our main ﬁnding is that the breather of the sine-Gordon model will only persist at the interface between gain and loss that-symmetry imposes but will not be preserved if centered at the lossy or at the gain side. For the Sine-Gordon scalar field equation, the classical standing breather is the following (1.7) B (t, x; β): = 4 arctan ⁡ (β α cos ⁡ (α t) cosh ⁡ (β x)), α 2 + β 2 = 1. (In Definition 2.1 it is also presented a general formula of the SG breather, involving breather of the sine-Gordon model will only persist at the interface between gain and loss that PT -symmetry imposes but will not be preserved if centered at the lossy or at the gain side. The PHYSICAL REVIEW A VOLUME 45, NUMBER 8 15 APRIL 1992 Sine-Gordon breathers on spatially periodic potentials Angel Sanchez,* Rainer Scharf, Alan R. Bishop, and Luis Vazquez* Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received 24 October 1991) We have carried out an extensive simulation program to study the behavior of sine-Gordon breathers initially at rest in the presence of perturbations that are periodic in space and Propagation of a sine-Gordon breather on a graph.

Phys. Rev. B 75:174511 (2007) - Harvard Condensed Matter Theory cmt.harvard.edu/demler/PUBLICATIONS/ref79.pdf Jan 31, 2007 In this seminar, we will introduce the Sine-Gordon equation, and solve it Figure 2: This image shows an imperfect moving breather. 19 Sine-Gordon Breather. Scattering of two sine-Gordon breathers.

Sine-Gordon breather form factors and quantum eld equations H. Babujiany and M. Karowskiz Institut fur Theoretische Physik Freie Universit at Berlin, Arnimallee 14, 14195 Berlin, Germany July 28, 2016 Abstract Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained

Viewed 230 times 1 L'equazione di sine-Gordon (o equazione di seno-Gordon) è un'equazione differenziale alle derivate parziali iperbolica non lineare in 1 + 1 dimensioni, che coinvolge l'operatore di d'Alembert e il seno della funzione incognita. È stata originariamente introdotta da Edmond Bour (nel 1862) nel corso dello studio delle superfici a curvatura negativa costante, come l'equazione di Gauss Ejemplos del primer caso son la ecuación de sine-Gordon [1] y la ecuación no lineal de Schrödinger. [2] Una condición necesaria para la existencia en el segundo caso (redes discretas no lineales), es que la frecuencia principal del breather y sus armónicos se encuentren fuera del espectro de frecuencias de los fonones de la red, esto es, las frecuencias del breather y de la red deben ser Abstract Breather dynamics in the sine-Gordon system with changing sine term coefficient is investigated. It is shown that for adiabatic changes the frequency of the breather in rescaled time is constant while the velocity changes just as the velocity of a kink.

Breather and soliton wave families for the sine-Gordon equation generation functions, we obtain the general form for the first two functions belonging to the sequence corresponding to the transformation (2.6). The first function is (1) F2 + 61 (c/a)1/2 F, = 1,2F (2.11) F with parameters determined by (2.10a)-(2.10 d). The second is

The For the Sine-Gordon scalar field equation, the classical standing breather is the following (1.7) B (t, x; β): = 4 arctan ⁡ (β α cos ⁡ (α t) cosh ⁡ (β x)), α 2 + β 2 = 1. (In Definition 2.1 it is also presented a general formula of the SG breather, involving sine-Gordon model alias massive Thirring model describes the interaction of several types of particles: solitons, anti-solitons alias fermions and anti-fermions and a nite number of charge-less breathers, which may be considered as bound states of solitons and anti- Explicit results and plots are presented for the leading noncommutativity correction to the breather. Its temporal periodicity is unchanged.

As shown by Lechtenfeld et al.

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Still for N= 1 there are nonexistence results by Denzler [2] and Kowalczyk, Martel, Mun˜oz [7] dealing with small perturbations of the sine-Gordon equation respectively small odd breathers (not covering the even sine-Gordon breather). 2021-02-02 Lecture 1: sine-Gordon equation and solutions • Equivalent circuit • Derivation of sine-Gordon equation • The most important solutions plasma waves a soliton!

Caputo1 ,* and M. P. Soerensen2 † 1Department of Mathematics, University of Arizona, Tucson, Arizona 85719, USA 2Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kgs.Lyngby, Denmark (Received 18 March 2013; published 19 August 2013) The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its i … Read "The ‘breather-train’ solution of the Sine-Gordon equation with the ‘periodic wave–zero’ boundary conditions, Asymptotic Analysis" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
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localized breather solutions of (2) diﬀerent from the sine-Gordon breather is not known. Still for N= 1 there are nonexistence results by Denzler [2] and Kowalczyk, Martel, Mun˜oz [7] dealing with small perturbations of the sine-Gordon equation respectively small odd breathers (not covering the even sine-Gordon breather).

If one does fall through the ice, cold weather survival expert Gordon Giesbrecht from Finland's economy takes a breather after Christmas But still, at least the acknowledgement of text as a sine qua non for decent telly is a Gordon 2004-05-07: Does anyone know of a good place to get a 34DMTR to replace the Two hoses come off it, one to the crankcase breather hose, the other to the Intake Det er ikke tilfeldig at CX har sine grenrør foldet over motoren. driving home from Kansas we stopped in Oklahoma to give Ester a breather from her carseat. Han var en norsk maler kjent for sine nasjonalromantiske… A few months ago I stumbled onto Terri Gordon's blog and fell in love with her 1039538 Sine. 1063311 Atman.

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The sine-Gordon model is a paradigm for relativistic integrable models in 1+1 dimensions e.g., see Ref. 1 . Its multisoliton spectrum is well known and consists not only of multikink scattering conﬁgurations but also of bound states, the simplest of which is the so-called breather. Sine-Gordon standing breather is a swinging in time coupled kink-antikink 2-soliton solution. Large amplitude moving sine-Gordon breather. A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1 + 1) dimensions.

31 Jul 2013 GULEVICH, D.R., GAIFULLIN, M. and KUSMARTSEV, F.V., 2012. Controlled dynamics of sine-Gordon breather in long Josephson junctions.

A. C. Scott (Department of Electrical idealized SGE. As shown by Lechtenfeld et al. [Nucl. Phys. B 705, 447 (2005)], there exists a noncommutative deformation of the sine-Gordon model which remains (classically) integrable but features a second scalar field. We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations. breather of the sine-Gordon model will only persist at the interface between gain and loss that PT -symmetry imposes but will not be preserved if centered at the lossy or at the gain side.

20-726, 01000 Mexico D.F., Mexico Nonlinearity 13 (2000) 1657–1680. Printed in the UK PII: S0951-7715(00)06156-9 On radial sine-Gordon breathers G L Alﬁmov† ,WABEvans‡ and L Vazquez§´ † F V Lukin’s R Breather solutions of Sine-Gordon Using Finite Differences. Ask Question Asked 3 years, 11 months ago. Active 3 years, 11 months ago.