EVOLUTION AND INTERACTIONS OF SOLITARY WAVES (SOLITONS) IN NONLINEAR DISSIPATIVE SYSTEMS

A generalized wave equation containing production and dissipation of e nergy is derived in a heuristic fashion so as to have in the dissipati onless limit the (two-way wave) Boussinesq equation, while for the slo wly evolving in a moving frame (one-way) wave system, it reduces to th e dissipation modified KDV equation (KDV-KSV) with the same energy-bal ance law. The new equation allows investigating the head-on collision of dissipative localized structures. A special difference scheme is de vised which faithfully represents the balance law for energy. The nume rical simulations show that if the production-dissipation rate is of o rder of a small parameter, the coherent structures upon collisions pre serve their localized character and within a time interval proportiona l to the inverse of the small parameter they behave like (imperfect) s olitons. The collisions are almost ideal without phase shift. The only difference from the strictly soliton collision is that during the tim e of interaction the dissipative structures are ''aging'' and changing their shapes.