Many-particle bound states in a Bose gas with a complex pair interaction between particles are considered. It is shown that the combination of attraction and repulsion between particles leads to the emergence of bound states with peculiar physical properties. In the limit of a large number of bound states in the Hartree approximation, these states are close in the structure and properties to exotic solitons (compactons and peakons) in classical systems with weak spatial dispersion. Examples of exotic solitons of various types in magnetically ordered media are considered. ©1998 American Institute of Physics.