Soliton Solutions of the Chen–Li–Liu Equation with an Arbitrary Refractive Index
https://doi.org/10.1134/S2304487X21040088
Abstract
The perturbed Chen–Li–Liu equation with an arbitrary refractive index describing the propagation of pulses in an optical fiber is considered. The traveling wave reduction is used to find a solution of this nonlinear partial differential equation. Separating the imaginary and real parts of the resulting equation and equating them to zero, a system of ordinary differential equations is constructed. The compatibility conditions of the system of ordinary differential equations are determined. Stationary points of the system of equations are found. Exact solutions of the mathematical model are obtained for n = 1 and 2 expressed in terms of the Jacobi and Weierstrass elliptic functions. It is shown that the solutions found in the case of an arbitrary refractive index have the form of periodic and solitary waves (optical solitons).
Keywords
perturbed Chen–Li–Liu equation,
arbitrary refractive index,
traveling wave,
exact solution,
optical soliton
Supporting agencies: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (state project) No. 0723-2020-0036, and was also financed by the Russian Foundation research project No. 18-29-10025
About the Authors
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
N. V. Ermolaeva
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute); Volgodonsk Engineering Technical Institute, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
347360
Moscow
Rostovskaya oblast
Volgodonsk
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Review
For citations:
Kudryashov N.A., Ermolaeva N.V. Soliton Solutions of the Chen–Li–Liu Equation with an Arbitrary Refractive Index. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(4):302-307. (In Russ.) https://doi.org/10.1134/S2304487X21040088
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