Classical Particlelike Behavior of Sine-Gordon Solitons in Scattering Potentials and Applied Fields

Fogel, M. B.; Trullinger, S. E.; Bishop, A. R.; Krumhansl, J. A.

doi:10.1103/physrevlett.36.1411

Cited by 148 publications

(34 citation statements)

References 7 publications

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“…It is by now well established, already from pioneering works in the seventies [6,7] that both types of kinks behave, under a wide class of perturbations, like relativistic particles. The relativistic character arises from the Lorentz invariance of their dynamics, see Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Collective coordinate approaches were introduced in [6,7] to describe kinks as particles (see [2,3,4,9] for a very large number of different techniques and applications of this idea). Although the original approximation was to reduce the equation of motion for the kink to an ordinary differential equation for a time dependent, collective coordinate which was identified with its center, it is being realized lately that other collective coordinates can be used instead of or in addition to the kink center.…”

Section: Introductionmentioning

confidence: 99%

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Length scale competition in nonlinear Klein—Gordon models: A collective coordinate approach

Cuenda

Sánchez

2005

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study the phenomenon of length scale competition, an instability of solitons and other coherent structures that takes place when their size is of the same order of some characteristic scale of the system in which they propagate. Working on the framework of nonlinear Klein-Gordon models as a paradigmatic example, we show that this instability can be understood by means of a collective coordinate approach in terms of soliton position and width. As a consequence, we provide a quantitative, natural explanation of the phenomenon in much simpler terms than any previous treatment of the problem. Our technique allows to study the existence of length scale competition in most soliton bearing nonlinear models and can be extended to coherent structures with more degrees of freedom, such as breathers.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Length scale competition in nonlinear Klein—Gordon models: A collective coordinate approach

Cuenda

Sánchez

2005

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The effects of a large variety of perturbations on the properties of that equation have been investigated (see [3,4] for recent reviews). However, starting from the seminal work by Fogel et al [5], only a few papers have been devoted to disordered systems, corresponding to the addition of certain properly chosen inhomogeneous terms to the original equation. In particular, a simple form of inhomogeneity, which to some extent is amenable to analytical work, is a spatially periodic, external potential.…”

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confidence: 99%

Sine-Gordon breathers on spatially periodic potentials

et al. 1992

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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 constant in time. We report here a number of different observed phenomena and the range of the relevant parameters (the ratio of the breather width to the perturbation wavelength and the perturbation magnitude) for which each one of them occurs. We also propose some qualitative explanations valid for certain regimes. PACS number(s): 03.40.KfThe study of nonlinear disordered systems has recently become the subject of a great deal of research [1]. A model that has been widely used as an approximate description of quasi-one-dimensional physical phenomena is the sine-Gordoll (SG) equation (see, for instance, [2] and references therein). The effects of a large variety of perturbations on the properties of that equation have been investigated (see [3,4] for recent reviews). However, starting from the seminal work by Fogel et al. [5], only a few papers have been devoted to disordered systems, corresponding to the addition of certain properly chosen inhomogeneous terms to the original equation. In particular, a simple form of inhomogeneity, which to some extent is amenable to analytical work, is a spatially periodic, external potential. The propagation of SG kinks on such a potential has been previously studied by Mkrtchyan and Shmidt [6] and Malomed and Tribelsky [7], and the same.problem has been analyzed as the limiting case of a spatial lattice of impurities when this lattice becomes very dense [8].. In this work we concern ourselves with the influence of these periodic potentials on the SG breathers. Some preliminary work has been done by Pascual [9]. We introduce this issue as an excellent example of the competition between two characteristic length scales, which is an ubiquitous phenomenon in real physical systems: In this case, these length scales are the breather width (AB) and the perturbation period (Ap). The aim of this work is twofold. First, our immediate goal is to learn whether the particle picture of solitons, often very useful, holds or not, and, if not, when and how it breaks down due to this perturbation; second, our ultimate purpose is to apply our results to nonlinear wave propagation in potentials which are stochastic in space (this problem has been considered in [10]), viewing the periodic potential as a particular component or "color" of the noisy one. As is explained below, understanding one color is a fundamental input to treating propagation in a general color distribution. On the other hand, we are also interested in comparing the phenomena we are describing here to those caused by the same kind of potential on the nonlinear Schrodinger (NLS) equation, often viewed as a weak 45 nonlinearity limit of the SG equation. Our investigations on this related system are planned to be reported elsewhere [11].To approach the above issues, we have carried out a number of numerical simulations spanning large intervals of the p...

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“…As a first step to understand this relationship, it is very important to have a well-established picture of soliton scattering in systems with few impurities, because localization generally originates from multiple interference between backscattered waves. Solitons, the well known self-localized waves which describe elementary nonlinear purposes [4]. This is so because the evolution equations, derived through some analytical approach, that govern their dynamics under the influence of perturbations, are commonly quite similar to those of particles under external forces.…”

Section: Introductionmentioning

confidence: 99%

Interference effects in soliton scattering by impurities

Kivshar¹,

Sánchez²,

Chubykalo³

et al. 1992

J. Phys. A: Math. Gen.

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Abstract. We present a comprehensive study ofthe effects of inhomogeneities on nonlinear excitation dynamics in different one-dimensional soliton-bearing systems. We theoretically analyse soliton scattering by one and two point-like impurities in the framework of the predict that interference effects arise in the form of an oscillatory dependence ofthe soliton reflection coefficient on the distance between impurities. The main fanor responsible for this behaviour is the spectral density of the soliton radiation: the values of that distance which are integer multiples of the main wavelength radiated by the soliton upon collision with the inhomogeneities give rise to resonant scattering, with very link reflection. Our approximate analytical predictions explain previous numerical results concerning nonlinear lattices, and are further supported by new simulations that we have performed on.thc sine-Gordon system.

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Classical Particlelike Behavior of Sine-Gordon Solitons in Scattering Potentials and Applied Fields

Cited by 148 publications

References 7 publications

Length scale competition in nonlinear Klein—Gordon models: A collective coordinate approach

Length scale competition in nonlinear Klein—Gordon models: A collective coordinate approach

Sine-Gordon breathers on spatially periodic potentials

Interference effects in soliton scattering by impurities

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