Collective coordinate analysis for double sine-Gordon model

Nazifkar, Samira; Javidan, Kurosh

doi:10.1590/s0103-97332010000100014

Cited by 8 publications

(12 citation statements)

References 12 publications

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“…Comparing the predictions with related numerical simulations has not been done in this paper. The general behavior of the soliton predicted in [41] is the same as what has been presented here. This means that two models describe the general features of the soliton-potential interaction correctly.…”

Section: Numerical Simulationsupporting

confidence: 74%

“…In our model, solitons have dynamical space dependent mass while the soliton mass in the model [41] is constant. Our presented model saves the symmetries and also topological properties of the theory in the presence of the external potential, but the model in [41] is not able to carry all of the field properties correctly. Note that the solitonic solution in the sine-Gordon model essentially establishes because of topological boundary conditions.…”

Section: Numerical Simulationmentioning

confidence: 99%

See 1 more Smart Citation

Interaction of Double Sine-Gordon Solitons with External Potentials: an Analytical Model

Nazifkar

Javidan

Sarbishaei

2016

Chinese Phys. Lett.

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Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to the model through a suitable nontrivial metric for the background space-time. The model is able to predict most of the features of the soliton-potential interaction. It is shown that a soliton can pass through a potential barrier if its velocity is greater than a critical velocity which is a function of soliton initial conditions and also characters of the potential. It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there. This situation is very important in applied physics. Solitonwell system has been investigated using the presented model too. Analytical results also have been compared with the results of the direct numerical solutions.

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Section: Numerical Simulationsupporting

confidence: 74%

Section: Numerical Simulationmentioning

confidence: 99%

Interaction of Double Sine-Gordon Solitons with External Potentials: an Analytical Model

Nazifkar

Javidan

Sarbishaei

2016

Chinese Phys. Lett.

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“…As a next example, let us deal with a more complex model for the diffusion coefficient. Such a model is derived from

this potential is known as double sine–Gordon model and it is applied to study ultra short optical pulses in He 3 [21] , [22] , in decaying of false vacuum and phase transitions in field theory [22] , [23] . The left panel of Fig.…”

Section: Solutionsmentioning

confidence: 99%

Diffusive process under Lifshitz scaling and pandemic scenarios

Anacleto

Brito

Queiroz

et al. 2020

Physica A: Statistical Mechanics and its Applications

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We here propose to model active and cumulative cases data from COVID-19 by a continuous effective model based on a modified diffusion equation under Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is rich enough to capture different aspects of a complex virus diffusion as humanity has been recently facing. The model being continuous it is bound to be solved analytically and/or numerically. So, we investigate two possible models where the diffusion coefficient associated with possible types of contamination are captured by some specific profiles. The active cases curves here derived were able to successfully describe the pandemic behavior of Germany and Spain. Moreover, we also predict some scenarios for the evolution of COVID-19 in Brazil. Furthermore, we depicted the cumulative cases curves of COVID-19, reproducing the spreading of the pandemic between the cities of São Paulo and São José dos Campos, Brazil. The scenarios also unveil how the lockdown measures can flatten the contamination curves. We can find the best profile of the diffusion coefficient that better fit the real data of pandemic.

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“…The notion we want to explore in this paper originates from the investigations already presented in some previous works [1,2] which where motivated by investigations introduced in [3,4], in which the scattering of solitons of integrable systems from the potentials have been studied. Similarly, solitary behaviour of coupled fields in the presence of an inhomogeneity is a thought-provoking phenomenon which will be considered in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…These effects can also be taken into account by making some parameters of the equation of motion to become a function of space or time [10,11]. Another way is to add an external potential to the field through the metric of background space-time [3,12,13]. This method can be used for models in which the Lagrangians are Lorentz invariant, such as sine-Gordon model, φ 4 theory, CP N model, NKG models etc.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of coupled field solitons: A collective coordinate approach

2014

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In this paper we consider a class of systems of two coupled real scalar fields in bidimensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate approach. First, we present the class of systems of the collective coordinate equations which are derived using the presented method. After that, we follow the dynamics of the coupled fields with local inhomogeneity like a delta function potential wall as well as a delta function potential well. The results of the investigation of the two coupled fields are compared to each other and the differences are discussed. The method can predict most of the characters of the interaction.

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Collective coordinate analysis for double sine-Gordon model

Cited by 8 publications

References 12 publications

Interaction of Double Sine-Gordon Solitons with External Potentials: an Analytical Model

Interaction of Double Sine-Gordon Solitons with External Potentials: an Analytical Model

Diffusive process under Lifshitz scaling and pandemic scenarios

Dynamics of coupled field solitons: A collective coordinate approach

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