# 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

1622 Breather-like structures in modified sine-Gordon models L A Ferreira1 and Wojtek J Zakrzewski 2 1 Instituto de Física de S ão Carlos, IFSC/USP, Universidade de S o Paulo, Caixa Postal 369, CEP 13560-970, São Carlos-SP, Brazil 2 Department of Mathematical Sciences, University of Durham, Durham DH1 3LE,

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. b) Breather outgoing speed for a well with L = 10, a = 0.2, v = = 0.1. The gaps correspond to other types of scattering. c) A solution profile for L = 2, a = 0.8, v = = 0.3 and x0 = 15.5. The breather is split into two: one is ejected from the well - "Scattering of sine-Gordon breathers on a potential well." 2021-03-12 Breather boundary form factors in sine-Gordon theory. Nuclear Physics B, 2011. Gábor Takács Fei et al.

D plasma waves. D a soliton! D chain of solitons. D resistive state.

## Denzler, J.: Nonpersistence of Breather solutions under perturbation of the sine Gordon equation. In: Proceedings on dynamical systems, Euler International Mathematical Institute, Sankt Petersburg, November 1991, ed. V.F. Lazutkin, to appear in Birkhäuser, Basel Google Scholar

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### 2 Jun 2016 Sine-Gordon model, through the method of lattice regularization. We will see there are soliton, antisoliton and breather solutions. For us, the

Nearly integrable perturbation methods are applied to infer approximate solution branches of space- and time-periodic breather trains of order one amplitude. These approximate solutions consist of coherent spatial structures, either homogeneous or with one breather per 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 … A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon equation and the focusing nonlinear Schrödinger equation are examples of one-dimensional partial differential equations that possess breather solutions. 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.

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.

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These functions are found to be bounded and periodic and affect the soliton velocity. The 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 OSTI.GOV Journal Article: Sine-Gordon breathers on spatially periodic potentials Physica D 189 (2004) 167–187 Evolution of two-dimensional standing and travelling breather solutions for the Sine–Gordon equation A.A. Minzonia, Noel F. Smythb,∗, Annette L. Worthyc 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 0,r 1] and absorb all outgoing radiation.

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### 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

Interaction between sine-Gordon breathers. 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.