Exact Solutions of the Differential Equation for Highly Dispersed Optical Pulses
https://doi.org/10.1134/S2304487X21020085
Abstract
A nonlinear partial differential equation describing the propagation of highly dispersed pulses in optical fibers is studied. Taking into account the Ablowitz–Ramani–Segur hypothesis, the reduction of the original partial differential equation to an ordinary differential equation is considered. Using the traveling wave variables, the ordinary differential equation is obtained in which the imaginary and real parts are separated from each other. Equating them to zero gives a system of ordinary differential equations. The integrability of this system is investigated using the Painlevé test. It is shown that the system of ordinary differential equations does not pass the Painlevé test, since there is only one integer Fuchs index. At the third step of the Painlevé test, the conditions for the compatibility of the system are found. Taking into account these conditions, the sixth-order ordinary differential equation is obtained. Exact solutions for the ordinary differential equation are constructed using the simplest equation method. The constructed solutions are expressed in terms of elliptic sine and exponential functions, and have the form of periodic and solitary waves, respectively.
Supporting agencies: The work was carried out with financial support Russian Foundation for Basic Research (project No. 18-29-10039) and the Ministry of Science and Higher Education of the Russian Federation (draft state assignment No. 0723-2020-0036)
About the Authors
D. V. Safonova
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:
Safonova D.V., Kudryashov N.A. Exact Solutions of the Differential Equation for Highly Dispersed Optical Pulses. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(2):143-150. (In Russ.) https://doi.org/10.1134/S2304487X21020085
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