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Year 2018, Volume: 8 Issue: 2, 425 - 437, 01.12.2018

Abstract

References

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  • Bayındır C., (2016) Sci. Rep., 6, 22100; doi: 10.1038/srep22100.
  • Bayındır C., (2015), TWMS Journal of Applied and Engineering Mathematics, 5-2, 298.
  • Bayındır C., (2015), Hesaplamalı Akı¸skanlar Mekani˘gi C¸ alı¸smaları i¸cin Sıkı¸stırılabilir Fourier Tayfı
  • Y¨ontemi, XIX. T¨urk Mekanik Kongresi, Trabzon. (In Turkish) Bayındır C., (2015), Okyanus Dalgalarının Sıkı¸stırılabilir Fourier Tayfı Y¨ontemiyle Hızlı Modellenmesi
  • XIX. T¨urk Mekanik Kongresi, Trabzon. (In Turkish) Cihan Bayındır for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.2.

COMPRESSIVE SPECTRAL RENORMALIZATION METHOD

Year 2018, Volume: 8 Issue: 2, 425 - 437, 01.12.2018

Abstract

In this paper a novel numerical scheme for nding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the governing equation is transformed into Fourier domain, but the iterations are performed for far fewer number of spectral components M than classical versions of the these methods with higher number of spectral components N . After the converge criteria is achieved for M components, N component signal is reconstructed from M components by using the l1 minimization technique of the compressive sampling. This method can be named as compressive spectral renormalization CSRM method. The main advantage of the CSRM is that, it is capable of nding the sparse self-localized states of the evolution equation s with many spectral data missing.

References

  • Schoellhamer, D. H., (2001), Geophysical Research Letters, 28, 16, 3187.
  • Stoica P., Li J., Ling J., (2009), IEEE Signal Processing Letters, 16, 241.
  • Thiele H. J., Nebeling M., (2007), Coarse Wavelength Division Multiplexing, CRC Press.
  • Walker S., (1986), Journal of Ligthwave Technology, 4, 8, 1125.
  • Comerford L., Kougioumtzoglou I. A., Beer M., (2016), Probabilistic Engineering Mechanics, 44, 66.
  • Ablowitz M. J., Musslimani Z. H., (2005), Optics Letters, 30, 16, 2140.
  • Zakharov V. E., (1968), Soviet Physics JETP, 2, 190.
  • Zakharov V. E., Shabat A. B., (1972), Soviet Physics JETP, 34, 62.
  • Bayındır C., (2009), MS Thesis, University of Delaware.
  • Canuto C, (2006), Spectral Methods: Fundamentals in Single Domains, Springer-Verlag.
  • Karjadi E. A., Badiey M, Kirby J. T., (2010), The Journal of the Acoustical Society of America, 127
  • Karjadi E. A., Badiey M, Kirby J. T., Bayındır C., (2012), IEEE Journal of Oceanic Engineering, 1, 112.
  • Trefethen L. N., (2000), Spectral Methods in MATLAB, SIAM.
  • Bayındır C., (2016), Physical Review E., 93, 032201.
  • Bayındır C., (2016), Physical Review E, 93, 062215.
  • Bayındır C., (2016), Physics Letters A, 380, 156.
  • Bayındır C., (2016), TWMS Journal of Applied and Engineering Mathematics, 6-1, 135.
  • Demiray H., Bayındır C., (2015), Physics of Plasmas, 22, 092105.
  • Bayındır C., (2016), arXiv Preprint, arXiv: 1604.06604.
  • Bayındır C., (2016), arXiv Preprint, arXiv: 1602.05339.
  • Bayındır C., (2016), arXiv Preprint, arXiv: 1602.00816.
  • Bayındır C., (2016), arXiv Preprint, arXiv: 1512.03584.
  • Petviashvili V. I., (1976), Soviet Journal of Plasma Physics JETP, 2, 257.
  • T. I. Lakoba, Yang J., (2007), Journal of Computational Physics, 226, 1668.
  • Fibich G., (2015), The Nonlinear Schrodinger Equation: Singular Solutions and Optical Collapse, Springer-Verlag.
  • Antar N., (2014), Journal of Applied Mathematics, 848153.
  • Goksel I., Antar N., Bakirtas I., (2018), Chaos, Solitons & Fractals, 109, 83.
  • Fleischer J. W., Segev M., Efremidis N. K., Christodoulides D. N., (2003) Nature, 422, 147.
  • Cand`es E. J., (2006), Proceedings of International Congress of Mathematicians, 3, 1433.
  • Cand`es E. J., Romberg ., Tao T., (2006), IEEE Transactions on Information Theory, 52, 489.
  • Bayındır C., (2016) Sci. Rep., 6, 22100; doi: 10.1038/srep22100.
  • Bayındır C., (2015), TWMS Journal of Applied and Engineering Mathematics, 5-2, 298.
  • Bayındır C., (2015), Hesaplamalı Akı¸skanlar Mekani˘gi C¸ alı¸smaları i¸cin Sıkı¸stırılabilir Fourier Tayfı
  • Y¨ontemi, XIX. T¨urk Mekanik Kongresi, Trabzon. (In Turkish) Bayındır C., (2015), Okyanus Dalgalarının Sıkı¸stırılabilir Fourier Tayfı Y¨ontemiyle Hızlı Modellenmesi
  • XIX. T¨urk Mekanik Kongresi, Trabzon. (In Turkish) Cihan Bayındır for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.2.
There are 35 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

C. Bayındır This is me

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

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