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It is found that dissipative types of stable soliton structures can exist in nonlinear optical media with broadband gain and group-velocity dispersion (GVD). These structures resemble ionization or combustion waves and are essentially self-accelerating pulses with a stationary-envelope form and a permanently shifting wave spectrum. Contrary to the conservative solitons, the dissipative ones exist for any sign of GVD. Being an attractor in the development of arbitrary initial distributions, the dissipative structures cause the fundamental Schr\"odinger solitons to disappear in the course of evolution in weakly nonconservative systems.
Vanin et al. (Fri,) studied this question.