Highly Dispersive Solitons Described by the System of Nonlinear Differential Equations Including a Bragg Grating
https://doi.org/10.56304/S2304487X20030049
Abstract
In nonlinear optics, great attention is currently paid to the analysis of nonlinear differential equations describing the propagation of solitary waves in optical media. In this work, the system of partial differential equations of the sixth order is studied to describe the propagation of two waves in a Bragg grating. This system includes nonlinearities of the third, fifth, and seventh degrees. To solve the problem, we apply the simplest equation method variance for finding solitary wave solutions. At the first step, the system is transformed to a system of ordinary differential equations by using the traveling wave variables. The resulting system is an overdetermined system consisting of four equations corresponding to the real and imaginary parts of the initial equations. From the equations corresponding to the imaginary parts, some restrictions for the parameters of initial partial differential equations are obtained. The pole order of the general solutions for the differential equations corresponding to the real parts is determined. This pole order allows us to use the simplest equations method to construct solutions in the form of solitary waves. Thus, the analytical solutions are constructed and graphs with different values of the mathematical model parameters are analyzed.
Keywords
Supporting agencies: The work was carried out with the financial support of RFBR grant No. 18-29-10025
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. Highly Dispersive Solitons Described by the System of Nonlinear Differential Equations Including a Bragg Grating. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(3):210-216. (In Russ.) https://doi.org/10.56304/S2304487X20030049
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