Stability of Time-Dependent Particlelike Solutions in Nonlinear Field Theories. II

Abstract

It is shown that particlelike solutions of the form ψ = φ(r)e−iωt to the nonlinear field ∇2ψ−c−2∂2ψ/∂t2=κ2ψ−μ2ψψ*ψ+λψψ*ψψ*ψcan exist for a certain range of the field parameters. The stability of the lowest-order solution of the above form is examined by first-order perturbation theory and also by direct integration of the perturbed field. Both methods indicate the existence of stable particlelike states, some of which have the further asset of a positive-definite energy density.