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

Nucl. Phys. B 705, 447 2005 , there exists a breather (i.e., not a standing wave) and the conditions under which it can persist in a -symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a -symmetric perturbation.

Download details: IP Address: 160.45.66.208 This content was downloaded on The noncommutative sine-Gordon breather André Fischera and Olaf Lechtenfelda Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany Received 17 November 2008; accepted 23 January 2009; published online 9 April 2009 As shown by Lechtenfeld et al. Nucl. Phys. B 705, 447 2005 , there exists a breather (i.e., not a standing wave) and the conditions under which it can persist in a -symmetric medium. 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.

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 K Bullough-Soliton Perturbations: A Variational

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. breather (i.e., not a standing wave) and the conditions under which it can persist in a -symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a -symmetric perturbation.

A numerical search for a stable oscillating mode in the $\phi ^4 $ equation similar to one that is known in the sine-Gordon equation has been carried out. Starting

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.

Full Record; Other Related Research We consider radial sine-Gordon kinks in two, three, and higher dimensions. A full two-dimensional simulation showing that azimuthal perturbations remain small allows us to reduce the problem to the one-dimensional radial sine-Gordon equation. We solve this equation on an interval [r, r1] and absorb all outgoing radiation. 2020-07-26 · 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. By means of direct simulations, it is found that the instability leads to a breakup of 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.
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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. 19 31 Jul 2013 GULEVICH, D.R., GAIFULLIN, M. and KUSMARTSEV, F.V., 2012.

We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations.
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2009-08-01 · In this letter, applying a novel approach, the extension of the homoclinic test approach , , , , , , to (1 + 1)D Sine–Gordon equation we obtain a new type of two-wave solution, homoclinic breather-wave solution, which is a homoclinic wave with breather effect. 2. Homoclinic breather-wave solution

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. 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. 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. The particularity of this simulation is that the sine-Gordon breather does not possess enough energy to pass through the junction.

In this work, we explore a prototypical example of a genuine continuum breather (i.e., not a standing wave) and the conditions under which it can persist in a PT-symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a PT-symmetric perturbation. Our main finding is that the breather of the sine-Gordon model will only persist at the interface

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.

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. 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.