Conditional stability of multiple-charged solitons

The stability of the three-dimensional multiple-charged soliton solutions to the nonlinear field equations is studied by Lyapunov's method. It is proved that an absolutely stable soliton solution can not exist in any field model. By imposing the subsidiary condition ΩpδQi=0 (fixation of charges) we find a sufficient condition for stability of the stationary soliton which includes the inequality ΩkΩi(∂Qi/∂Ωk<0. An illustrative example is considered. © 1984 Plenum Publishing Corporation.