STABILITY OF WALKING VECTOR SOLITONS

The stability of two-parameter families of walking vector solitons of coupled nonlinear Schrodinger equations in investigated. It is shown t hat all known, lowest-order soliton types, namely, slow, fast, vector in phase, and vector out of phase are dynamically stable in certain re gions of the parameter space. The condition of linear marginal stabili ty of the solitons is not necessarily given by an explicit geometric c riterion, because soliton instability mediated by the existence of com plex eigenvalues of the corresponding Lyapunov operator is found to oc cur also. [S0031-9007(98)07659-5].