Schemes for Generating Different Nonlinear Schrodinger Integrable Equations and Their Some Properties

In the paper, we want to derive a few of nonlinear Schrodinger equations with various formats and investigate their properties, such as symmetries, single soliton solutions, multi-soliton solutions, and so on. First of all, we propose an efficient and straightforward scheme for generating nonisospectral integrable hierarchies of evolution equations for which a generalized nonisospectral integrable Schrodinger hierarchy (briefly GNISH) singles out, from which we get a derivative nonlinear Schrodinger equation, a generalized nonlocal Schrodinger integrable system and furthermore we investigate the symmetries and conserved qualities of the GNISH. Next, we apply the dbar method to obtain a generalized nonlinear Schrodinger-Maxwell-Bloch (GNLS-MB) equation and its hierarchy by introducing a generalized Zakhrov-Shabat spectral problem, whose soliton solutions and gauge transformations are obtained.