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2021-03-22 · This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The

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. We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations. Explicit results and plots are presented for 2021-03-22 · This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation.

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This paper considers the damped, driven sine-Gordon equation with even, periodic boundary conditions on a finite length. Nearly integrable perturbation methods are applied to infer approximate solu Mar 12, 2021 In this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in. The double sine-Gordon equation is considered in the case of a small parameter multiplying the half-angle sine. It is shown that initial distributions consis The sine-Gordon Kink (red) and This is the sine-Gordon breather for: ep = 0.9. It was observed that the breather solution looked a lot like a bound state of two  Sep 8, 1998 The approach of Steuerwald–Lamb for obtaining exact solutions of the sine– Gordon equation is further developed through transformations by  The sine-Gordon (sG) equation is a partial differential equation, which is defined as solutions that behave like the sum of a kink and a breather as t → ±∞. The discrete Frenkel-Kontorova model, having the sine-Gordon equation as the continuous analog, was investigated numerically at a small degree of  calculation of the threshold for the applied forceto keep the breather alive. Several perturbation treatments of sine-Gordon breathers have been presented,.

1063311 Atman. 1246698 Helmet 1284478 Leo Kottke & Mike Gordon.

We compare form factors in sine-Gordon theory, obtained via the bootstrap, to finite volume matrix elements computed using the truncated conformal space ap-proach. For breather form factors, this is essentially a straightforward application of a previously developed formalism that describes the volume dependence of operator

For a passive termination the breather is reflected into a breather of less energy; when the characteristic impedance of the line equals the external load resistor the breather is almost annihilated. We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation.

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 $\begingroup$ I'm attempting

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. The influence of a boundary on a breather traveling in a Josephson line cavity is examined by means of numerical computations.

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 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 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 Fei et al. in the sine-Gordon (SG) [51] and φ4 [52] models.
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We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations.

Mai 2012 1/23 The influence of a boundary on a breather traveling in a Josephson line cavity is examined by means of numerical computations. For a passive termination the breather is reflected into a breather of less energy; when the characteristic impedance of the line equals the external load resistor the breather is almost annihilated. breather of the sine-Gordon model will only persist at the interface between gain and loss that PT -symmetry.
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The Sine Gordon Equation. In[1]:= Clear "Global' " There are also multi-soliton solutions, which we don't show, and a "breather" solu- tion, a bound soliton-anti 

As our model of interest, we will explore the sine-Gordon equation in the presence of a -symmetric perturbation. Our main finding is that the breather of the sine-Gordon model will only persist at A breather is a localized periodic solution of either continuous media equations or discrete lattice equations.