Analytical and Numerical Solution of the Generalized Nonlinear Schrödinger Equation with an Arbitrary Refractive Index
https://doi.org/10.1134/S2304487X21050072
Abstract
The propagation of solitary waves described by the generalized nonlinear Schrödinger equation with an arbitrary refractive index is investigated. The Cauchy problem for the considered equation cannot be solved; for this reason, traveling wave variables are used to find an analytical solution. These variables reduce the partial differential equation to a system of nonlinear ordinary differential equations. A solution of the resulting system of differential equations in the form of solitary waves is found using the simplest equation method. The numerical solution is constructed taking into account the discretization of the problem in time variable using a split-step method and by means of a finite difference in the space variable. The found analytical solution is used to verify the numerical solution of the solitary wave propagation problem described by the generalized nonlinear Schrödinger equation with periodic boundary conditions. Analytical and numerical solutions are plotted and these plots are analyzed taking into consideration the constraints on the parameters of the mathematical model.
About the Authors
K. V. Kan
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:
Kan K.V., Kudryashov N.A. Analytical and Numerical Solution of the Generalized Nonlinear Schrödinger Equation with an Arbitrary Refractive Index. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(5):412-417. (In Russ.) https://doi.org/10.1134/S2304487X21050072
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