title: Exact analytical solutions for the variational equations derived from the nonlinear Schrödinger equation.
abstract: By means of the variational formalism for the nonlinear Schrödinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrödinger equation.
authors.affiliation: Département de Physique de l'Université des Sciences et Techniques de Masuku, B.P. 943 Franceville, Gabon. K.Nakkeeran@abdn.ac.uk
authors.forename: A B
authors.initials: AB
authors.lastname: Moubissi
authors.forename: K
authors.initials: K
authors.lastname: Nakkeeran
authors.forename: Abdosllam M
authors.initials: AM
authors.lastname: Abobaker