Solitary Wave Solutions of the Coupled Nonlinear Schrödinger Equation with Cubic–Quintic–Septic Nonlinearity
https://doi.org/10.56304/S2304487X20050090
Abstract
The mathematical model for describing the propagation of pulses in a nonlinear optical fiber with Bragg gratings is considered. The analytical properties of the model of wave propagation in the forward and backward directions in fiber Bragg gratings, described by coupled generalized nonlinear Schrödinger equations with qubic–quintic–septic nonlinearities, are studied. Using the traveling wave variables, the transition to the system of four ordinary differential equations obtained for the real and imaginary parts of the original system of equations is carried out. The compatibility condition for two linear differential equations of the system under study is presented. For two nonlinear differential equations of the system under study, first integrals are obtained, as well as constraints on the parameters for which the system does not contain fractional powers, and compatibility conditions under which the system has a general solution. Under the found constraints on the parameters of the model, the solution of the studied system of four ordinary differential equations is presented. The solution is given in the form of an optical soliton for coupled nonlinear partial differential equations of the Schrödinger type with nonlinearities of the third, fifth, and seventh degrees. The found solution is illustrated for different values of the parameters.
Keywords
optical solitons,
exact solutions of differential equations,
nonlinear Schrödinger equation,
fiber
Bragg gratings
Supporting agencies: The research was carried out at the expense of a grant from the Russian Science Foundation (project No. 18-11-00209)
About the Authors
A. A. Kutukov
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:
Kutukov A.A., Kudryashov N.A. Solitary Wave Solutions of the Coupled Nonlinear Schrödinger Equation with Cubic–Quintic–Septic Nonlinearity. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(5):438-441. (In Russ.) https://doi.org/10.56304/S2304487X20050090
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