Self-maintained solitary waves in nonequilibrium media

We construct an original model of the propagation of waves of weak but finite amplitude, initiated by a nonequilibrium exothermic process that is associated with chemical reaction or relaxation in a medium. The medium may be single-phase (gaseous) or two-phase (liquid with bubbles). We construct a nonlinear differential model describing the wave-kinetic interaction and evolution of the waves. The linear dispersive and dissipative properties of these systems are studied both analytically and numerically. Particular attention is devoted to clarifying the physical mechanism of the solitary self-maintained wave formation regime; in the terminology of synergetics this wave can be termed a dissipative structure.