NUMERICAL STUDY OF SOLITON SOLUTIONS OF THE CUBIC-QUINTIC-SEPTIC NONLINEAR SCHRÖDINGER EQUATION
https://doi.org/10.26583/vestnik.2024.310
EDN: PVZUYF
Abstract
The problem of pulse propagation described by the nonlinear Schrödinger equation with non-Kerr nonlinearity of the third, fifth and seventh powers is considered. Optical solitons of the considered equation are found using simplest equations method and implicit functions method. The area of acceptable model parameters is illustrated. A modification of the split-step Fourier method is presented. Optical soliton propagation process is studied numerically. The validity of analytical calculations has been proven. The process of the interaction of a soliton pulse with a disturbance in the initial condition is analyzed. The process of the soliton pulse propogation in a medium with a random noise simulated. The stability of optical solitons of the cubic-quintic-septic nonlinear Schrodinger equation is proved. The influence of higher nonlinearity terms on the nonlinear Schrodinger equation solitary waves is studied. The soliton collisions in the presence of higher nonlinear terms are simulated. It is shown that in the presence of higher nonlinear terms, the solitons interact inelastically upon collision.
Keywords
Cubic-quintic-septic nonlinear Schrödinger equation,
Split-step Fourier scheme,
Optical soliton,
Numerical modeling,
Nonlinear optics,
Nonlinear differential equations
Supporting agencies: The study was supported by a grant from the Russian Science Foundation No. 23-41-00070, https://rscf.ru/project/23-41-00070/
About the Authors
V. A. Medvedev
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Supplementary files
Review
For citations:
Medvedev V.A., Kudryashov N.A. NUMERICAL STUDY OF SOLITON SOLUTIONS OF THE CUBIC-QUINTIC-SEPTIC NONLINEAR SCHRÖDINGER EQUATION. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(2):83-96. (In Russ.) https://doi.org/10.26583/vestnik.2024.310. EDN: PVZUYF
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