Analytical formulation for soliton-potential dynamics

Abstract

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.

12 pages, 10 figures

References in corpus (4)

• Interaction of topological solitons with defects: using a nontrivial metric
• Dynamical properties of a Soliton in a Potential Well
• Scattering of topological solitons on holes and barriers
• Scattering of Topological Solitons on Barriers and Holes in Two λϕ^4 Models

Cited by in corpus (13)

• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• Soliton-potential interaction in the nonlinear Klein-Gordon model
• Improved model for the topological soliton-potential interaction in Phi^4 Model
• Collective coordinate variable for soliton-potential system in sine-Gordon model
• Collective-coordinate analysis of inhomogeneous nonlinear Klein-Gordon field theory
• An introduction to kinks in ${\phi }^4$-theory
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• On multichannel solutions of nonlinear Schrödinger equations: algorithm, analysis and numerical explorations
• Emergence of oscillons in kink-impurity interactions
• Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential
• Excitation of high-amplitude localized nonlinear waves as a result of interaction of kink with attractive impurity in sine-Gordon equation
• Bubble nucleation around heterogeneities in ${\varphi }^4$-field theories