The mapping approach is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations, the remarkable characteristics of which is that we can have infinitely different ansatzs and thus end up with the abundance of solutions. The traditional ways are to map on the basis of travelling wave reduction, i.e., on the basis of ordinary differential equations. Recently, we have successfully extended this method to the mapping on the variable-coefficients non-traveling wave reduction. Using an improved Riccati mapping approach, we obtain new exact solutions for the (1+1)-dimensional related to Schrdinger equation. Based on the derived solutions, the nonpropagating light solitons(temporal light soliton and bight-dark pulse light soliton), propagating light solitons, and the neutralisation phenomena of light-solitons were constructed.