ANALYTICAL AND NUMERICAL MODELLING OF SOLITARY WAVES DE-SCRIBED BY THE GENERALIZED KAUP–NEWELL EQUATION
https://doi.org/10.26583/vestnik.2023.254
Abstract
Pulse propagation in optical fiber described by the generalized Kaup–Newell equation with arbitrary refractive index is investigated. Using traveling wave variables the generalized Kaup–Newell equation is reduced to a system of nonlinear differential equations. Compatibility conditions for the system of equations are found. Exact solutions of the equation with fixed n = 1 expressed by an elliptic Weierstrass function and an elliptic sine are obtained. Using the generalized simplest equation method, exact solutions of the equation in the form of solitary waves are found for an arbitrary refractive index. Mathematical model with periodical boundary conditions is formulated. Using pseudo-spectral method the numerical solution on a regular grid is constructed. The program code of the numerical solution for the problem is verified by comparing the numerical solution with the analytical one in the form of solitary waves. The error dependence on a step of grid is studied taking into account the restrictions on the model parameters. Figures of analytical and numerical solutions were constructed and analyzed.
About the Authors
K. V. Kan
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
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Review
For citations:
Kan K.V., Kudryashov N.A. ANALYTICAL AND NUMERICAL MODELLING OF SOLITARY WAVES DE-SCRIBED BY THE GENERALIZED KAUP–NEWELL EQUATION. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(2):83-89. (In Russ.) https://doi.org/10.26583/vestnik.2023.254
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