STATIONARY SOLITON BOUND-STATES EXISTING IN RESONANCE WITH LINEAR WAVES

The phenomenon of stable propagation of spatially localized solitary w aves, has been investigated for various dynamical systems. If a solito nlike pulse is in resonance with linear waves, then this pulse emits r adiation and therefore it cannot exist as a stationary wave. Neverthel ess, it is shown here that two (or more) radiating (and thus nonexisti ng as stationary waves) single solitonlike pulses can still form a sta tionary bound state due to mutual trapping of their own radiation. Tra pped radiation forms a standing wave, which in turn produces local min ima in an effective interaction potential of the neighboring solitons. However, in contrast to conventional solitons, soliton bound states t hat 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 localised solutions, and they are inherently unstable. Tw o physically important systems for which stationary bound states of ra diating solitons can be found are considered.