Stationary soliton bound states existing in resonance with linear waves

The phenomenon of stable propagation of spatially localized solitary waves, has been investigated for various dynamical systems. If a solitonlike pulse is in resonance with linear waves, then this pulse emits radiation and, therefore, it cannot exist as a stationary wave. Nevertheless, it is shown here that two (or more) radiating (and thus nonexisting as stationary waves) single solitonlike pulses can still form a stationary bound state due to mutual trapping of their own radiation. Trapped radiation forms a standing wave which, in turn, produces local minima in an effective interaction potential of the neighboring solitons. However, in contrast to conventional solitons, soliton bound states that are formed due to trapped radiation exist only for discrete values of soliton parameters, i.e., such bound states do not form continuous families of localized solutions, and they are inherently unstable. Two physically important systems for which stationary bound states of radiating solitons can be found are considered.