Collective coordinate variable for soliton-potential system in sine-Gordon model (original) (raw)

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

Chinese Physics Letters, 2016

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.

Collective coordinate analysis for double sine-Gordon model

Brazilian Journal of Physics, 2010

Collective coordinate analysis for adding a space dependent potential to the double sine-Gordon model is presented. Interaction of solitons with a delta function potential barrier and also delta function potential well is investigated. Most of the features of interaction are derived analytically. We will find that the behaviour of a solitonic solution is like a point particle which moves under the influence of a complicated effective potential. The effective potential is a function of the field initial conditions and also parameters of added external potential.

Ju l 2 00 8 A new model for the soliton-potential systems

2009

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle ’living’ under the influence of a complicated potential which is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.

Soliton Stability In a Generalized Sine-Gordon Potential

International Journal of Theoretical Physics, 2004

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations can be cast in terms of a Schrödinger-like operators for fluctuations and their spectra are calculated.

Dynamics of sine-Gordon solitons

After reviewing a few physical examples in which the sine-Gordon equation arises as the governing dynamical equation, we discuss various solutions exhibiting multisoliton dynamics. Interaction of solitons and the corresponding velocitydependent interaction potentials are derived and discussed. Numerical experiments are carried out in order to study kink dynamics in an inhomogeneous medium. Finally, we introduce two kinds of generalized sine-Gordon equations and discuss their properties.

A new model for the soliton-potential interaction

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle living under the influence of a complicated potential which is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.

Soliton Solutions in a Modified Double and Triple Sine-Gordon Models

2016

We modify both the double sine-Gordon (DSG) and triple sine-Gordon (TSG) model in (1,1) dimensions by the addition of an extra kinetic term and a potential term to their Lagrangian density and present a modified DSG (MDSG) and a modified TSG (MTSG) models. We obtain soliton solutions of the presented modified models and find that both of them possesses the same solutions of the unmodified model with some extra conditions imposed on the parameters of the models. We study some properties of the modified models, in particular, we show that the corresponding governing equation has two solutions, a special ones, which are the exact solutions of the unmodified models and a general ones, and these two types of solutions are coincides in our presented models. We end the paper with conclusions and some features and comments.

Soliton–potential interaction in the nonlinear Klein–Gordon model

Physica Scripta, 2012

Interaction of solitons with external potentials in nonlinear Klein-Gordon field theory is investigated using an improved model. Presented model is constructed with a better approximation for adding the potential to the lagrangian through the metric of background spacetime. The results of the model are compared with the another model and the differences are discussed. *

Radiation From a Sine-Gordon Soliton Propagating in an External Potential

The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We examine the radiation emitted due to the interaction of the soliton with the potential and we calculate the potential dependent part of the time evolution equation for the creation and annihilation operators for fluctuations.

Analytical formulation for soliton-potential dynamics

Physical Review E, 2008

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle living under the influence of a complicated potential which is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.