A Perturbation Expansion for the Nonlinear Schrödinger Equation with Application to the Influence of Nonlinear Landau Damping

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Abstract
The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schrödinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method to those by Ott and Sudan on the KdV equation and to a recent paper by Pereira and Stenflo.