Interacting sine-Gordon solitons and classical particles: A dynamic equivalence

Bowtell, Graham; Stuart, Allan E. G.

doi:10.1103/physrevd.15.3580

Cited by 29 publications

(20 citation statements)

References 15 publications

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“…Solitons in field theory are described in general by their moduli (collective coordinates) representing their locations and momenta. An identical particle-like interpretation turns out to hold for singularities (this has been argued in a series of papers [9,10]). In our string theory representation the singular soliton coordinates map directly into coordinates associated with spike configurations.…”

Section: Jhep06(2009)064mentioning

confidence: 82%

Moduli dynamics of AdS₃strings

Jevicki

Jin

2009

J. High Energy Phys.

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Section: Jhep06(2009)064mentioning

confidence: 82%

Moduli dynamics of AdS₃strings

Jevicki

Jin

2009

J. High Energy Phys.

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“…By numerically integrating the ODEs that govern the trajectories of the quasiparticles, we constructed an approximate two-soliton profile, showing that the quasi-particles obey a pseudoNewtonian, more precisely Machean, law. Then, the quasi-particle dynamics and the coarse-grain solution were compared to the exact dynamics [9] and the analytical two-soliton solution, respectively. In both cases, excellent quantitative and qualitative agreement was obtained.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we provide numerical results, based on the coarse-grain description of the soliton-soliton and soliton-antisoliton interactions, and benchmark them against the exact results in [9]. Though a quantitative comparison cannot be made because no scales are provided on the plots in [9], we can still perform a qualitative comparison.…”

Section: Quasi-particle Dynamicsmentioning

confidence: 99%

“…Though a quantitative comparison cannot be made because no scales are provided on the plots in [9], we can still perform a qualitative comparison.…”

Section: Quasi-particle Dynamicsmentioning

confidence: 99%

“…Here, we must note that Bowtell & Stuart [9] developed a method, based on the poles of the Hamiltonian density, that allowed them to compute the exact (ODEs for the) trajectories of the centers of the solitons. Their technique has not been applied to any other well-known nonlinear wave equations, which makes the SGE unique from the point of view of availability of reference solution for the trajectories of the centers to establish the practical applicability of the present approach.…”

Section: The Sine-gordon Equation and Its Soliton Solutionsmentioning

confidence: 99%

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Physical dynamics of quasi-particles in nonlinear wave equations

Christov

2008

Physics Letters A

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By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.

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The Application of Biomaterials in the Treatment of Platinum‐Resistant Ovarian Cancer

2019

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More than 70 % of women with ovarian cancer are diagnosed with advanced‐stage disease, which is initially treated with cytoreductive surgery, and combination chemotherapy with platinum‐based compounds. Most patients initially respond to platinum‐based therapy, but eventually up to 80 % of this responsive cohort becomes refractory due to the development of platinum resistance. This review discusses current and potential therapeutic approaches that exploit biomaterial‐based applications to combat platinum resistance either by enhancing the delivery of platinum‐based drugs or prodrugs, delivering other toxic non‐platinum‐based bioactive factors (by themselves or in combination with platinum‐based drugs) or by delivering other bioactive factors that re‐sensitize resistant ovarian cancer cells to these drugs. The types of materials that are used, the bioactive factors applied (i.e., drug or gene delivery), and the specific agents that are employed to target these types of cancer cells are discussed. We conclude that the unique attributes of biomaterial‐based applications can be further explored toward overcoming platinum‐resistant ovarian cancer as monotherapy, or in combination with other treatment strategies.

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Interacting sine-Gordon solitons and classical particles: A dynamic equivalence

Cited by 29 publications

References 15 publications

Moduli dynamics of AdS₃strings

Moduli dynamics of AdS₃strings

Physical dynamics of quasi-particles in nonlinear wave equations

The Application of Biomaterials in the Treatment of Platinum‐Resistant Ovarian Cancer

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Interacting sine-Gordon solitons and classical particles: A dynamic equivalence

Cited by 29 publications

References 15 publications

Moduli dynamics of AdS3strings

Moduli dynamics of AdS3strings

Physical dynamics of quasi-particles in nonlinear wave equations

The Application of Biomaterials in the Treatment of Platinum‐Resistant Ovarian Cancer

Contact Info

Product

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Moduli dynamics of AdS₃strings

Moduli dynamics of AdS₃strings