Abstract
In this paper, the inhomogeneous nonlinear Schrödinger equation with the loss/gain and the frequency chirping is considered. The N-solitary solution is presented by employing the Darboux transformation. As an example, the explicit soliton solution on continuous wave (cw) background with the loss/gain and the frequency chirping is generated, and two exact analytic solutions that describe (i) modulation instability and (ii) soliton propagation on a cw background with the loss/gain and the frequency chirping are in detail discussed.
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