Quintic B-spline collocation method for the generalized nonlinear Schrödinger equation

In this study, the generalized nonlinear Schrödinger (GNLS) equation is solved numerically by the quintic B-spline collocation finite element method. In the method, Crank-Nicolson scheme is used for the time integration, and the space variable is discretized by means of quintic B-spline functions. Finally, we investigate properties of the numerically computed solutions of the GNLS equation; in particular we study the generation of solitary waves, interaction of solitons and blow up.