The soliton: A new concept in applied science

Scott, Alwyn C.; Chu, Flora Y. F.; McLaughlin, David W.

doi:10.1109/proc.1973.9296

Cited by 1,546 publications

(406 citation statements)

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“…Breathers describe soliton-antisoliton bound states [19]. In the rest frame the classical solution corresponding to the nth quantum state reads [17,19] …”

Section: Particle Mass Spectramentioning

confidence: 99%

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088Rev. D 11, (1975. According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants β 2 > 8π. The consequence of this theorem would be the non-existence of the quantum ground state of the sineGordon model for β 2 > 8π. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for β 2 > 8π. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model. *

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“…Breathers describe soliton-antisoliton bound states [19]. In the rest frame the classical solution corresponding to the nth quantum state reads [17,19] …”

Section: Particle Mass Spectramentioning

confidence: 99%

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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“…(31) is PDE, its solution exists. This well-known solution, existing for PQ > 0, is [15,47,48] FS ; τ ðÞ ¼ A e sech S À u e τ L e exp iu e S À u c τ ðÞ…”

Section: Mechanical Models Of Microtubulesmentioning

confidence: 99%

Mechanical Models of Microtubules

Zdravković¹

2018

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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Microtubules are the major part of the cytoskeleton. They are involved in nuclear and cell division and serve as a network for motor proteins. The first model that describes nonlinear dynamics of microtubules was introduced in 1993. Three nonlinear models are described in this chapter. They are longitudinal U-model, representing an improved version of the first model, radial φ-model and new general model. Also, two mathematical procedures are explained. These are continuum and semi-discrete approximations. Continuum approximation yields to either kink-type or bell-type solitons, while semidiscrete one predicts localized modulated waves moving along microtubules. Some possible improvements and suggestions for future research are discussed.

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“…no reflection). Given that fact, it is natural to ask what might happen with solitons in the nonlinear sine-Gordon model (for details concerning solitons, see for example [6]. A soliton travelling in the positive x direction (rapidity θ) is given by expressions…”

Section: Classical Scattering and Solitonsmentioning

confidence: 99%

Purely transmitting integrable defects

Corrigan

2006

Czech J Phys

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The soliton: A new concept in applied science

Cited by 1,546 publications

References 189 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Mechanical Models of Microtubules

Purely transmitting integrable defects

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The soliton: A new concept in applied science

Cited by 1,546 publications

References 189 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Mechanical Models of Microtubules

Purely transmitting integrable defects

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Product

Resources

About

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?