COMPRESSIVE SPECTRAL RENORMALIZATION METHOD

Bayindir C.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, cilt.8, sa.2, ss.425-437, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 2
  • Basım Tarihi: 2018
  • Dergi Adı: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.425-437
  • Anahtar Kelimeler: Spectral renormalization, Petviashivili's method, compressive sampling, spectral methods, nonlinear Schrodinger equation, WAVES, SOLITONS
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

In this paper a novel numerical scheme for finding 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 l(1) 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 finding the sparse self-localized states of the evolution equation(s) with many spectral data missing.