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Article information
2015 , Volume 20, ¹ 3, p.99-108
Chekhovskoy I.S.
Using Pade approximation for solving systems of nonlinear Schrodinger equations by the split-step Fourier method
Purpose. This paper presents a new modification of the well-known split-step Fourier method. The development of telecommunication technologies caused the necessity to solve numerically new types of systems of coupled nonlinear Schrodinger equations. For devices with strong coupling between the modes of light, such as multicore optical fibers, there is a need to consider the linear coupling between the various modes. Presented numerical algorithm can solve the NSE system, taking into account such linear coupling. Methodology. Pade approximation for the numerical calculation of the matrix exponential was used. The matrix exponential appears in the generalization of the split-step Fourier method to the system of coupled NSE. Pade approximation formula uses the approximation of exponential by rational functions with polynomials of degree 6 in the numerator and the denominator and having the 13th-order accuracy. Findings. The new modification of split-step Fourier method and its parallel implementation based on the Intel MKL library are represented. In this paper we demonstrate the high accuracy of the proposed numerical algorithm on the solution of scalar NSE in the form of fundamental soliton. The possibility of efficient parallelization of the algorithm for computing systems with shared memory was demonstrated by the figures with the acceleration of the algorithm on different numbers of threads. Originality/value. The proposed new numerical algorithm can effectively solve the problem of propagation of light pulses in multi-core and multi-mode optical fibers. The possibility of creating its parallel implementation allows using this algorithm on a large spectrum of computing systems with shared memory.
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Keywords: split-step Fourier method, Pade approximation, nonlinear Schrodinger equation, multi-core fibers, multi-mode fibers, nonlinear fiber optics
Author(s):
Chekhovskoy Igor Sergeevich
Position: Student
Office: Novosibirsk State University, Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk
E-mail: igor428m@gmail.com
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Bibliography link:
Chekhovskoy I.S. Using Pade approximation for solving systems of nonlinear Schrodinger equations by the split-step Fourier method // Computational technologies. 2015. V. 20. ¹ 3. P. 99-108
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