We present a novel projection operator method for deriving the ordinary differential equations (ODEs) which describe the pulse parameters dynamics of an ansatz function for the nonlinear Schrodinger equation. In general, each choice of the phase factor theta in the projection operator gives a different set of ODEs. For theta = 0 or pi/2, we prove that the corresponding projection operator scheme is equivalent to the Lagrangian method or the bare approximation of the collective variable theory. Which set of ODEs best approximates the pulse parameter dynamics depends on the ansatz used. (C) 2004 Elsevier B.V. All rights reserved.
- nonlinear Schrodinger equation
- optical fibers
- Lagrangian variational method
- ordinary differential equations
- projection operator method
- collective variable