Exactly integrable nonlinear Schrodinger equation models withvarying dispersion, nonlinearity and gain: application for solitondispersion

We show that the methodology based on the generalized inverse scattering transform (IST) concept provides a systematic way to discover the novel exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain or absorption. The fundamental innovation of the present approach is to notice that it is possible both to allow for a variable spectral parameter with new dependent variables and to apply of the famous "moving in time focuses" concept of the self-focusing theory to the IST formalism. We show that for nonlinear optics this algorithm is a useful tool to design novel dispersion managed fiber transmission lines and soliton lasers. Fundamental soliton management regimes are predicted