Compressive split-step Fourier method

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Tarih

2015-02-09

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Yayıncı

Işık University Press

Erişim Hakkı

info:eu-repo/semantics/openAccess

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Özet

In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can be used as a very efficient tool for the split-step spectral simulations of various phenomena which can be modeled by using differential equations. The proposed method depends on the idea of using a smaller number of spectral components compared to the classical split-step Fourier method with a high number of components. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique with l(1) minimization, it is shown that the sparse signal can be reconstructed with a significantly better efficiency compared to the classical split-step Fourier method. Proposed method can be named as compressive split-step Fourier method (CSSFM). For testing of the proposed method the Nonlinear Schrodinger Equation and its one-soliton and two-soliton solutions are considered.

Açıklama

Anahtar Kelimeler

Compressive sampling, Nonlinear Schrodinger equation, Sparse signals, Split step Fourier method, Equation

Kaynak

TWMS Journal of Applied and Engineering Mathematics

WoS Q Değeri

N/A

Scopus Q Değeri

Cilt

5

Sayı

2

Künye

Bayındır, C. (2015). Compressive split-step Fourier method. Journal of Applied and Engineering Mathematics, 5(2), 298-306.