INTERNAL-MODES OF ENVELOPE SOLITONS

We extend the concept of internal mode to envelope solitons and show t hat this mode is responsible for long-lived, weakly damped periodic os cillations of the soliton amplitude observed in numerical simulations. We present analytical and numerical results for solitons of the gener alized nonlinear Schrodinger equation and analyze the example of the c ubic-quintic nonlinearity in more detail. We obtain also analytical cr iteria for the existence and bifurcations of the soliton internal mode and calculate the rate of the radiation-induced damping of the solito n oscillations induced by excitation of the internal mode. Copyright ( C) 1998 Elsevier Science B.V.