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The concept of soliton complex in a nonlinear dispersive medium is formulated. It is shown that interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher order spatial or mixeddoi:10.5488/cmp.2.2.255 fatcat:gqvl6kforzffvekienpzpcfkt4