Internal dynamics of the double-sine-Gordon chain

Burdick, S.; El‐Batanouny, M.; Willis, C. R.

doi:10.1103/physrevb.34.6575

Cited by 14 publications

(11 citation statements)

References 22 publications

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“…The internal dynamics of multiple and single DSG soliton configurations using molecular dynamics have been studied in [9]. There have also been studies about kink anti-kink collision processes for DSG equation [20].…”

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confidence: 99%

Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

et al. 2009

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The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter ǫ. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1 + 1 dimension.We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions.Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter ǫ is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.

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confidence: 99%

Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

et al. 2009

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“…Condensed matter applications include the spin dynamics of superfluid He 3 , magnetic chains, commensurate-incommensurate phase transitions, surface structural reconstructions, and domain walls. In quantum field theory and quantum optics DSG equation applications include quark confinement and self-induced transparency, respectively, see [22,23]. The double sine-Gordon (DSG) equation has the potential,…”

Section: The Double Sine-gordon (Dsg) Equationmentioning

confidence: 99%

“…In the physical applications, the nonlinear force f(u) also has other forms [20][21][22][23][24][25] …”

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confidence: 99%

Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain

Han

Zhang

2008

Journal of Computational Physics

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“…The double-Sine-Gordon (DSG) equation which is a generalization of the ordinary Sine-Gordon (SG) equation has been the focus of much recent investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. It has been shown to model a variety of systems in condensed matter, quantum optics, and particle physics [2].…”

Section: Introductionmentioning

confidence: 99%

“…Condensed matter applications include the spin dynamics of superfluid 3 He [3, 4], magnetic chains [5], commensurateincommensurate phase transitions [6], surface structural reconstructions [7], and domain walls [8,9] and fluxon dynamics in Josephson junction [10].In quantum field theory and quantum optics, DSG applications include quark confinement [11] and self-induced transparency [12]. The internal dynamics of multiple and single DSG soliton configurations using molecular dynamics have been studied in [2]. There have also been studies about kink anti-kink collision processes for DSG equation [13].…”

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confidence: 99%

Static properties of multiple-sine-Gordon systems

2010

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In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of periodic functions.Next, periodic and step-like solutions of these systems are discussed in some details.In particular, we study the static properties of such systems by considering slope and phase diagrams. We also use concepts like energy density and pressure to characterize and distinguish such solutions. We interpret these solutions as an interacting many body system, in which kinks and antikinks behave as extended particles. Finally, we provide a linear stability analysis of periodic solutions which indicates short wavelength solutions to be stable. PACS: 05.45.Yv, 05.00.00, 02.60.Lj, 24.10.Jv I. INTRODUCTION The double-Sine-Gordon (DSG) equation which is a generalization of the ordinary Sine-Gordon (SG) equation has been the focus of much recent investigations [1-15]. It has been shown to model a variety of systems in condensed matter, quantum optics, and particle physics [2]. Condensed matter applications include the spin dynamics of superfluid 3 He [3, 4], magnetic chains [5], commensurateincommensurate phase transitions [6], surface structural reconstructions [7], and domain walls [8,9] and fluxon dynamics in Josephson junction [10].In quantum field theory and quantum optics, DSG applications include quark confinement [11] and self-induced transparency [12]. The internal dynamics of multiple and single DSG soliton configurations using molecular dynamics have been studied in [2]. There have also been studies about kink anti-kink collision processes for DSG equation [13]. One can also point to the statistical mechanics applications [14], and perturbation theory for this system [15]. Following our pervious study on the periodic and step-like solutions of DSG equation[1], we focus on a generalization of this system with the self-interaction potential (see Fig.1) *

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Internal dynamics of the double-sine-Gordon chain

Cited by 14 publications

References 22 publications

Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain

Static properties of multiple-sine-Gordon systems

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