This article construct several soliton solutions to highly dispersive NLSE with CQS nonlinearity. A number of integration algorithms have produced a wide spectrum of soliton possible. As byproduct of these integration schemes, several additional solutions such as periodic and Jacobi’s elliptic function solutions also emerge. These are also listed, in order to gain a more complete spectrum of solutions of the model. These solutions serve as an encouragement to further proceed along with identifying highly dispersive solitons in other models. Immediate extension is to study models with birefringence and DWDM networks. Other aspects also need to be addressed in the present model. These include the demonstration of the conservation laws of the model and the integration of the model with the inclusion of perturbative terms.