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

It is shown that particlelike solutions of the form ψ = φ(r)e^−iωt to the nonlinear field $${\nabla }^2{\mathrm{\psi -c}}^{\text{−2}}{\partial }^2{\mathrm{\psi /\partial t}}^2{\mathrm{=\kappa }}^2{\mathrm{\psi -\mu }}^2{\mathrm{\psi \psi }}^{*}{\mathrm{\psi +\lambda \psi \psi }}^{*}{\mathrm{\psi \psi }}^{*}\psi$$ can 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.