Behavior of different ansätze in the generalized projection operator method

Using the recently reported generalized projection operator method for the nonlinear Schrodinger equation, we derive the generalized pulse parameters equations for ansatze like hyperbolic secant and raised cosine functions. In general, each choice of the phase factor theta in the projection operator gives a different set of ordinary differential equations. For theta = 0 or theta = pi/2, the corresponding projection operator scheme is equivalent to the Lagrangian variation method or the bare approximation of the collective variable theory. We prove that because of the inherent symmetric property between the pulse parameters of a Gaussian ansatz results the same set of pulse parameters equations for any value of the generalized projection operator parameter theta. Finally we prove that after the substitution of the ansdtze function, the Lagrange function simplifies to the same functional form irrespective of the ansdtze used because of a special property shared by all the anatze chosen in this work. (c) 2005 Elsevier Ltd. All rights reserved.