Solitary waves in active-dissipative dispersive media

Abstract
Solitary waves in active-dissipative dispersive media are considered. The exact solutions in the form of solitary waves and kink-shaped waves are presented. The difference equation for numerical simulation of nonlinear waves is given. Numerical results of the interaction of solitary waves are discussed. It is shown that there is a solitary wave in active-dissipative dispersive media that has the soliton property.