Solitons as dissipative structures

I review here recent results regarding the excitation of nonlinear interfacial oscillations, and hence waves, at the surface of a liquid or at the interface separating two liquids when a thermal gradient is imposed or there is adsorption, and subsequent absorption in the bulk, of a (light) surfactant, hence creating tangential stresses due to the surface tension gradient (Marangoni effect). I also recall their solitonic features upon collisions and boundary reflections, etc., even though the proposed evolution equations are not hyperbolic but a parabolic–hyperbolic combination like a dissipation-modified Boussinesq–Korteweg–de Vries equation. Theory, numerics, and experiments support my claim that solitons can exist and survive in a dissipative medium provided, for example, past an instability threshold, there is an appropriate input–output energy balance. This is very much like (steady) dissipative structures and, indeed, (nonlinear) waves traveling with constant velocity in the moving frame are steady dissipative structures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004