Stability criterion for stationary bound states of solitons with radiationless oscillating tails

We investigate stationary bound states of bright solitary waves in an optical fiber with fourth-order dispersion, which is described by a generalized nonlinear Schr\"odinger equation with an additional fourth-order derivative term. It is shown that various families of two-soliton (and multisoliton) bound states exist for this equation in the parameter region where single solitons have radiationless oscillatory tails. We analyze and discuss their stability and possible applications. A stability criterion for stationary two-soliton (and multisoliton) states of a conservative Hamiltonian dynamical system is derived.