Optical Solitons Described by a System of the Fourth Order Nonlinear Differential Equations with Nonlocal Nonlinearity
https://doi.org/10.56304/S2304487X20050053
Abstract
A system of nonlinear partial differential equations of the fourth order with nonlocal nonlinearity is investigated. The system of equations describes the propagation of two waves in an optical fiber. The Cauchy problem for the considered system is unsolvable by the inverse scattering method. Traveling wave variables are used to transform the system of partial differential equations to a system of ordinary differential equations of the fourth order. The simplest equation method is applied to seed exact solutions in the form of solitary waves. The transformed system of ordinary differential equations consists of four equations, corresponding to the real and imaginary parts of the initial system. Constraints on the parameters of the initial model are found. The system of differential equations corresponding to the real parts is considered together with the determined constraints. Compatibility conditions for the system are found. One of the equations corresponding to the real part is studied taking into account the constraints for the parameters obtained from compatibility conditions. Exact solutions in the form of solitary waves are found. Graphs of the solutions obtained at different parameter values of the initial system of equations with the determined constraints are constructed. The influence of the mathematical model parameters on the behavior of solutions is analyzed.
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. Optical Solitons Described by a System of the Fourth Order Nonlinear Differential Equations with Nonlocal Nonlinearity. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(5):449-454. (In Russ.) https://doi.org/10.56304/S2304487X20050053
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