JAEM 2015, Vol 5, No 2
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Öğe Book Review: Oktay Veliyev. Multidimensional Periodic Schrödinger Operator (Perturbation Theory and Applications)(Işık University Press, 2015) Hasanoğlu, Elman[No abstract available]Öğe Compressive split-step Fourier method(Işık University Press, 2015-02-09) Bayındır, CihanIn 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.
