Applications of the weighted scheme for GNLS equations in solving soliton solutions

Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically, which is achieved using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrödinger equations. The characteristic behavior of the nonlinearity admitted in the system has been investigated and the soliton state of the system in the limit ofα → 0 andα → ∞ has been studied. The results presented show that soliton phenomena are characteristics associated with the nonlinearities of the dynamical systems.