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

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

Breather Initial Conditions. ϕinit(x,y,z)=4 tan−1(cos(γvvt)vcosh(γvx))+δϕfluc(x,y,z)γv≡1√1+v2. v=1 In this paper, we review sine-Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living cellular Sine-Gordon Breather. Scattering of two sine-Gordon breathers. Scattering of Kortweg-Devries solitons on a periodic grid. Lecture Notes.

Sine gordon breather

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.

chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets.

Our main ﬁnding is that the breather of the sine-Gordon model will only persist at 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. 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).

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

The breather is split into two: one is ejected from the well - "Scattering of sine-Gordon breathers on a potential well." Figure 1: a) Breather position for a well with L = 2, a = 0.2, v = = 0.1 and x0 = 29.92. The particularity of this simulation is that the sine-Gordon breather does not possess enough energy to pass through the junction.

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.
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Together they form a unique fingerprint. TY - JOUR AU - Denzler, Jochen TI - Second order nonpersistence of the sine Gordon breather under an exceptional perturbation JO - Annales de l'I.H.P.

Lecture Notes. Low-intensity light pulses in optical fibers propagate linearly but dispersively (as described in “Solitons in the Sine-Gordon Equation”). This dispersion tends to 7 Feb 2018 loops show the performance of the scheme for kinks and breathers initial tial differential equations; graph theory; sine–Gordon equation. 31 Jan 2007 In this seminar, we will introduce the Sine-Gordon equation, and solve it Figure 2: This image shows an imperfect moving breather.
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Collision and penetration of solitons, antisolitons and breathers. This solution of the sine-Gordon equation is called a breather for obvious reasons.

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.

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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.