Avner Peleg and Yeojin Chung 2003 J. Phys. A: Math. Gen. 36 10039 doi:10.1088/0305-4470/36/39/305
Avner Peleg and Yeojin Chung
Show affiliationsWe study stationary solutions of the nonlinear Schrödinger equation in the presence of small but non-zero third-order dispersion (TOD). Using a singular perturbation theory around the ideal soliton we calculate these solutions up to the second order in the TOD coefficient. The existence and linear stability of the stationary solutions is proved for any finite order of the perturbation theory. The results obtained by our numerical simulations of the nonlinear Schrödinger equation are in very good agreement with theory. The significance of these results for fibre optic communication systems is discussed.
42.65.Tg Optical solitons; nonlinear guided waves
35Q55 NLS-like (nonlinear Schrödinger) equations (See also 37K10)
Issue 39 (3 October 2003)
Received 9 May 2003, in final form 12 June 2003
Published 17 September 2003
Avner Peleg and Yeojin Chung 2003 J. Phys. A: Math. Gen. 36 10039
Gregory S Mitchell and Simon R Cherry 2009 Phys. Med. Biol. 54 1291
Sung-Joon Ye et al 2004 Phys. Med. Biol. 49 387
Tom Timusk and Bryan Statt 1999 Rep. Prog. Phys. 62 61
Yeojin Chung and Avner Peleg 2005 Nonlinearity 18 1555
Patrick J Sutton et al 2003 Class. Quantum Grav. 20 S815
Steven H. Pravdo and Stuart B. Shaklan 2009 ApJ 700 623
Jacob L. Bean et al. 2010 ApJ 711 L19
Lydia B Austin and Bruce M Shore 1995 Phys. Educ. 30 41
A M Akulshin et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 491