Collective-Coordinate Analysis of Inhomogeneous Nonlinear Klein–Gordon Field Theory

Abstract

Two different sets of collective-coordinate equations for solitary solutions of nonlinear Klein–<br><br>Gordon (NKG) model are introduced. The collective coordinate equations are derived using different<br><br>approaches for adding the inhomogeneities as external potentials to the soliton equation of motion.<br><br>The interaction of the NKG field with a local inhomogeneity like a delta function potential wall or a<br><br>delta-function potential well is investigated using the presented collective-coordinate equations, and the results of the two different models are compared. Most of the characters of the interaction are derived analytically. The analytical results are also compared to the results of numerical simulations.