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Optics Letters

Optics Letters


  • Vol. 30, Iss. 16 — Aug. 15, 2005
  • pp: 2140–2142

Spectral renormalization method for computing self-localized solutions to nonlinear systems

Mark J. Ablowitz and Ziad H. Musslimani  »View Author Affiliations

Optics Letters, Vol. 30, Issue 16, pp. 2140-2142 (2005)

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A new numerical scheme for computing self-localized states - or solitons - of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.

© 2005 Optical Society of America

OCIS Codes
(000.0000) General : General
(000.2690) General : General physics

Mark J. Ablowitz and Ziad H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005)

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  1. G. Stegeman and M. Segev, Science 286, 1518 (1999). [CrossRef]
  2. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003). [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Elsevier, 2001).
  4. A. W. Snyder, D. J. Mitchell, L. Polodian, and F. Ladouceur, Opt. Lett. 16, 21 (1991).
  5. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997). [CrossRef]
  6. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003). [CrossRef]
  7. V. I. Petviashvili, Sov. J. Plasma Phys. 2, 257 (1976).
  8. B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970).
  9. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, 1981).
  10. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998)
  11. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001). [CrossRef]
  12. M. J. Ablowitz and Z. H. Musslimani, Physica D 184, 276 (2003). [CrossRef]
  13. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 67, 025601(R) (2003). [CrossRef]
  14. Z. H. Musslimani and J. Yang, J. Opt. Soc. Am. B 21, 973 (2004). [CrossRef]
  15. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003). [CrossRef]
  16. N. K. Efremidis, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003). [CrossRef]
  17. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, Opt. Lett. 29, 1530 (2004). [CrossRef]
  18. T. Peschel, U. Peschel, and F. Lederer, Phys. Rev. E 57, 1127 (1998). [CrossRef]
  19. S. Darmanyan, A. Kobyakov, and F. Lederer, Phys. Rev. E 57, 2344 (1998). [CrossRef]
  20. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004). [CrossRef]
  21. Z. Xu, Y. V. Kartashov, L. Crasovan, D. Mihalache, and L. Torner, Phys. Rev. E 71, 016616 (2005). [CrossRef]

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