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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. For more details on the scheme, please, refer to: https://hal.archives-ouvertes.fr/hal-01160840/ Sine-Gordon Breather Dynamics Alwyn C. Scott Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706, U.S.A. Received June 14, 1978;final version September 27, 1978 Abstract SineGordon breather dynamics. A. C. Scott (Department of Electrical idealized SGE. As shown by Lechtenfeld et al. [Nucl.

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. 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.

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 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 latter dynamics is found to be interesting in its own right giving rise to kink-antikink pairs on the gain side and complete decay of the breather on the Denzler, J.: Nonpersistence of Breather solutions under perturbation of the sine Gordon equation.

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.

For more details on the scheme, please, refer to: https://hal.archives-ouvertes.fr/hal-01160840/ The particularity of this simulation is that the sine-Gordon breather does not possess enough energy to pass through the junction. Thus, it is confined to th 2021-02-02 Sine-Gordon Breather Dynamics To cite this article: Alwyn C Scott 1979 Phys. Scr. 20 509 View the article online for updates and enhancements. Related content Solitons in Condensed Matter Physics A R Bishop-Soliton-Like Spin Waves in 3 He B P W Kitchenside, P J Caudrey and R … 2009-08-01 Lecture 1: sine-Gordon equation and solutions • Equivalent circuit • Derivation of sine-Gordon equation • The most important solutions plasma waves a soliton!

Lecture 1: sine-Gordon equation and solutions • Equivalent circuit • Derivation of sine-Gordon equation • The most important solutions plasma waves a soliton! chain of solitons resistive state breather and friends • Mechanical analog: the chain of pendula • Penetration of magnetic ﬁeld Introduction to the ﬂuxon dynamics in LJJ Nr. 2

As the kink shrinks OSTI.GOV Journal Article: Interaction between sine-Gordon breathers. Interaction between sine-Gordon breathers. Full Record; Other Related Research The deformed NLS model for two-soliton solutions [6, 7] and the deformed sine-Gordon model for two-kink and breather solutions exhibit this property. In the context of the Riccati-type method there have been shown that the deformed SG, KdV and NLS models [ 8 , 9 , 10 ], respectively, possess linear system formulations and that they exhibit infinite towers of exact non-local conservation laws. Breather solutions of Sine-Gordon Using Finite Differences.

Ask Question Asked 3 years, 11 months ago. Active 3 years, 11 months ago. Viewed 230 times 1 We develop a perturbation theory that describes bound states of solitons localized in a confined area. External forces and the influence of inhomogeneities are taken into account as perturbations to exact solutions of the sine-Gordon equation. We have investigated two special cases: a fluxon trapped by a microresistor and decay of a breather under dissipation. We have also carried out 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.
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For breather form factors, this is essentially a straightforward application of a previously developed formalism that describes the volume dependence of operator The rigidity of sine‐gordon breathers The rigidity of sine‐gordon breathers Birnir, Björn; McKean, Henry P.; Weinstein, Alan 1994-08-01 00:00:00 HENRY P. McKEAN Courant Institute AND ALAN WEINSTEIN University of California at Berkeley 1.
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We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit.

V.F. Lazutkin, to appear in Birkhäuser, Basel Google Scholar Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. Formulae for the asymptotic behavior of bosonic form factors are presented which are motivated by Weinberg’s 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.

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

We analyse the scattering of sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well.

We show that the breather can pass through the well and exit with a speed different, sometime larger, from the initial one. It can 2009-09-01 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 2007-01-15 Figure 1: a) Breather position for a well with L = 2, a = 0.2, v = = 0.1 and x0 = 29.92.