Abstract
We investigate the generalized higher-order nonlinear Schrödinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multisoliton solutions are presented by employing the Darboux transformation based on the Lax pair. As an example, we consider a soliton control system, and the results show that the soliton control system may relax the limitations to parametric conditions. The stability of the solution is discussed numerically; the results reveal that finite initial perturbations, such as amplitude, chirp, or white noise, could not influence the main character of the solution. In addition, the evolution of a quite arbitrary Gaussian pulse and the interaction between neighboring pulses have been studied in detail.
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