STABILITY OF THE NUMERICAL SOLUTION OF THE FOURTH ORDER GENERALIZED NONLINEAR SCHRÖDINGER EQUATION WITH CUBIC-QUINTIC-SEPTIC-NONIC NONLINEARITY
https://doi.org/10.26583/vestnik.2023.292
Abstract
A model of nonlinear optics described by the generalized fourth-order Schrödinger equation with nonlinearities of the third, fifth, seventh and ninth degrees is considered. An analysis of the stability in the first approximation of the exact solution of this model in the form of a monochromatic wave is carried out. Analysis of stability in the first approximation allows us to obtain the condition for the instability of the exact solution. The split-step Fourier method is used to numerically solve the model. An analysis of the stability in the first approximation of the solution of the numerical model in the form of a monochromatic wave corresponding to the exact solution of the analytical model is carried out. The instability condition in the first approximation of the solution of the numerical model in the form of a monochromatic wave is derived. It is demonstrated that from the fulfillment of the instability condition in the first approximation, obtained for the exact solution in the form of a monochromatic wave, the fulfillment of the instability condition for the numerical solution follows, while the converse is not true. A condition is given for the time step of the numerical model, under which the instability conditions in the first approximation for the numerical and analytical solutions coincide.
Supporting agencies: This research was supported by Russian Science Foundation Grant No. 22- 11-00141.
About the Authors
A. A. Bayramukov
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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Review
For citations:
Bayramukov A.A., Kudryashov N.A. STABILITY OF THE NUMERICAL SOLUTION OF THE FOURTH ORDER GENERALIZED NONLINEAR SCHRÖDINGER EQUATION WITH CUBIC-QUINTIC-SEPTIC-NONIC NONLINEARITY. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(6):332-338. (In Russ.) https://doi.org/10.26583/vestnik.2023.292
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