Decay to bound states of a soliton in a well

Kälbermann, G.

doi:10.1016/s0960-0779(00)00037-0

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…The effects of the external potential can be added to the equation of motion by using a suitable definition for λ(x), like λ(x) = 1 + v(x) [20,21,22]. For a constant value of parameter (λ(x) = 1) equation (3.9) reduces to (2.2) and therefore (2.3) is its exact solution.…”

Section: Nonlinear Klein-gordon Equationmentioning

confidence: 99%

Soliton–potential interaction in the nonlinear Klein–Gordon model

Saadatmand¹,

Javidan²

2012

Phys. Scr.

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Section: Nonlinear Klein-gordon Equationmentioning

confidence: 99%

Soliton–potential interaction in the nonlinear Klein–Gordon model

Saadatmand¹,

Javidan²

2012

Phys. Scr.

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“…In [22] a moduli space approximation was proposed which also takes account of the degrees of freedom of the well. See [15] for related work on the λφ 4 kink. Our calculations imply that the an additional degree of freedom could be the slope of the soliton at the centre of the kink as parametrized by a and b.…”

Section: Discussionmentioning

confidence: 99%

“…Soliton interactions with rectangular wells have also been discussed for various other soliton systems [3,4,5,6,10,11,21]. A kink interacting with a smooth well is discussed in [13] in terms of the sine-Gordon model and in [15] for the λφ 4 model. While these papers address the dynamics of a kink interacting with a well, multi-kinks interacting with wells have so far not been investigated.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of multi-kinks in the presence of wells and barriers

Goatham,

Mannering,

Hann

et al. 2010

Preprint

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Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with spacedependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with wells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.

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“…Nonclassical behavior in the scattering of topological solitons from potential wells has been obtained in [19][20][21][22][23], including a rich outcome structures of trapping, transmission and reflection as a function of the initial velocity. In the present work we investigate in detail the dynamics of NLS solitons impinging on potential wells with variable shapes.…”

mentioning

confidence: 99%

“…2. The possible escape of a soliton from a trapped state into a propagating state due to absorption of radiation has been predicted in [22].…”

mentioning

confidence: 99%

Resonant scattering of nonlinear Schrödinger solitons from potential wells

2004

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The interaction of nonlinear Schrödinger solitons with extended inhomogeneities, modeled by potential wells with different shapes, is investigated numerically. For fixed initial velocities below the transmission threshold, the scattering pattern as a function of the width of the well exhibits periodically repeating regions of trapping, transmission, and reflection. The observed effects are associated with excitation and a following resonant deexcitation (in the cases of escape) of shape oscillations of the solitons at the well boundaries. The analysis of the oscillations indicates that they are due to interference of the solitons with emitted dispersive waves.

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Decay to bound states of a soliton in a well

Cited by 5 publications

References 7 publications

Soliton–potential interaction in the nonlinear Klein–Gordon model

Soliton–potential interaction in the nonlinear Klein–Gordon model

Dynamics of multi-kinks in the presence of wells and barriers

Resonant scattering of nonlinear Schrödinger solitons from potential wells

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