Related papers: Collective Coordinate Methods and Their Applicabil…
We compare numerical solutions to the full field equations to simplified approaches based on implementing three collective coordinates for kink-antikink interactions within the $\varphi^4$ and $\phi^6$ models in one time and one space…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
Two different sets of collective-coordinate equations for solitary solutions of Nonlinear Klein-Gordon (NKG) model is introduced. The collective-coordinate equations are derived using different approaches for adding the inhomogeneities as…
Collective coordinates provide a powerful tool for separating collective and elementary excitations, allowing both to be treated in the full quantum theory. The price is a canonical transformation which leads to a complicated starting point…
A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as…
We consider constructing the relativistic system of collective coordinates of a field theory soliton on the basis of a simple principle: The collective coordinates must be introduced into the static solution in such a way that the equation…
A Collective coordinate variable for adding a space dependent potential to the sine-Gordon model is presented. Interaction of solitons with a delta function potential barrier and also delta function potential well is investigated. Most of…
We generalize effective energy variational techniques to study appropriately quantized solitonic field configurations. Our approach rests on collective quantization ideas and is specifically designed for the numerical evaluation of soliton…
We develop a consistent relativistic generalization of collective coordinate quantization of field theory solitons. Our principle of introducing collective coordinates is that the equations of motion of the collective coordinates ensure…
In this paper, we explored a class of potentials with three minima that support kink solutions exhibiting one long-range tail. We analyzed antikink-kink interactions using an effective Lagrangian based on collective coordinates and compared…
The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode…
An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the…
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the…
A field theoretical perturbation theory in inverse powers of coupling constant is developed which is manifestly covariant in every order of the expansion. A dilatation operator serves as an evolution dynamical one in a scale non-invariant…
We study kink scattering processes in the (1+1)-dimensional $\varphi^6$ model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities…
The evaluation of collective modes is fundamental in the analysis of molecular dynamics simulations. Several methods are available to extract that information, i.e normal mode analysis, principal component and spectral analysis of…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parameterize a manifold of zero modes and more…
Coupling the fields may lead to the emergence of new phenomena. In the realm of classical fields and nonlinear systems, extensive research has been conducted on their solitary and soliton solutions. In the conducted studies, typically two…
The collective coordinates approximation for the kink/anti-kink scattering in the $1+1$ dimensional $\phi^4$ model is considered and we discuss how the results found in the current literature on the topic can be improved by giving the…