Lyapunov stability of scalar charged solitons

The direct Lyapunov method is used to investigate the stability of charged solitons of pulson type described by a relativistic complex scalar field in a model of general form. It is shown that the stability can only be conditional. Some necessary and sufficient conditions for stability of stationary solitons for a fixed charge are formulated. Examples of models with power-law and logarithmic nonlinearities are considered. © 1981 Plenum Publishing Corporation.