Dark and Bright Solitons of the Nonlinear Schrödinger Equation with Saturation
https://doi.org/10.56304/S2304487X22010023
Abstract
A generalized model of the Schrödinger equation is considered to describe the propagation of pulses in a nonlinear medium with saturation. The Cauchy problem for it is not solved by the inverse scattering transform; the solution of the equation is considered including the travelling wave. A system of differential equations for the imaginary and real parts has been derived in terms of the traveling wave variables. Optical solitons for describing the propagation of pulses are obtained in the form of implicit functions. Analytical solutions are expressed in terms of an exponential function. The solutions obtained for light and dark solitons in a saturating medium of the generalized nonlinear Schrödinger equation are solitary waves under certain restrictions on the model parameters. The solutions obtained are plotted.
Supporting agencies: The work was carried out with financial support Russian Science Foundation (Project No. 22-11-00141 “Development of analytical and numerical methods for modeling waves in dispersive wave- waters")
About the Authors
E. V. Antonova
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
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Review
For citations:
Antonova E.V., Kudryashov N.A. Dark and Bright Solitons of the Nonlinear Schrödinger Equation with Saturation. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(1):22-27. (In Russ.) https://doi.org/10.56304/S2304487X22010023
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