Group Analysis of the Fourth-Order Differential Equation for Describing Optical Pulses
https://doi.org/10.1134/S2304487X21050096
Abstract
The fourth-order partial differential equation with power-law nonlinearities is investigated. It is used to describe the propagation of highly dispersed pulses in optical fibers. A group analysis of this equation is performed and the group transformations allowed by the differential equation are constructed in three steps. In the first step, a system of governing equations is obtained. In the second step, the coordinates of a tangent vector field are sought for. In the third step, infinitesimal generators are constructed. As a result, two infinitesimal generators allowed by the equation are found. Thus, it is shown that the considered equation is invariant under space and time translations. This indicates that the dimension of the original partial differential equation can be lowered by considering its reduction in traveling wave variables. As a result, an ordinary differential equation is obtained.
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 task 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. Group Analysis of the Fourth-Order Differential Equation for Describing Optical Pulses. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(5):403-406. (In Russ.) https://doi.org/10.1134/S2304487X21050096
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