Compressive Split-Step Fourier Method

Compressive Split-Step Fourier Method

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Abstract

In this paper an approach for decreasing the computational eort 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 ecient tool for the split-step spectral simulations of various phenomena which can be modeled by using dierential 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 l1 minimization, it is shown that the sparse signal can be reconstructed with a signicantly better eciency 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.

Keywords

Compressive sampling, nonlinear Schrodinger equation, sparse signals, splitstep Fourier method.