Soltary Wave Solutions of the Generalized Nonlinear Schrödinger Equation with Cubic, Quintic, and Septic Nonlinearities
https://doi.org/10.1134/S2304487X20020054
Abstract
The family of nonlinear Schrödinger equations describes a number of physical phenomena. The simulation and analysis of the propagation of highly dispersive optical pulses with allowance for several non-linearity types are currently of great interest. The dispersion is determined by the order of the governing equation. In this work, we consider the sixth order equation with cubic, quintic, and septic nonlinearities is analyzed. The search for solitary waves propagating in a nonlinear medium plays an important role in the study of the propagation of optical pulses. To solve this problem, the method based on the search for solitary wave solutions is used. At the first step, the substitution of travelling wave variables reduces the initial equation to the system of two differential equations corresponding to the real and imaginary parts of the initial equation. Restrictions on the parameters have been obtained from the equation corresponding to the imaginary part. The pole order of the equation corresponding to the real part has been determined. A nonzero pole order makes it possible to find solitary wave solutions at the next step. These solutions have been constructed and plots of solutions at different parameters have been analyzed.
Keywords
solitary waves,
Schrödinger equation,
nonlinear differential equations,
pulse propagation,
optical fiber
Supporting agencies: The work was carried out with the financial support of the RNF grant No. 18-11-00209
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. Soltary Wave Solutions of the Generalized Nonlinear Schrödinger Equation with Cubic, Quintic, and Septic Nonlinearities. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):110-114. (In Russ.) https://doi.org/10.1134/S2304487X20020054
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