Abstract
This chapter deals with the Gabitov-Turitsyn at the next higher order. This means that the multiple-scale expansion that was seen in Chapter 7, will now be carried out to O(z 2 a ). This gives a better accuracy and to the approximation that is described by the GTE seen in Chapter 7. In this technique, the pulse in the Fourier domain will be decomposed into a slowly evolving amplitude and a rapid phase that describe the chirp of the pulse. The fast phase is calculated explicitly that is driven by the large variations of the dispersion about the average. The amplitude evolution will be described by the nonlocal integro-differential evolution equations that is known as the higher order Gabitov-Turitsyn equation (HO-GTE).
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References
M. J. Ablowitz & H. Segur. Solitons and the Inverse Scattering Transform. SIAM. Philadelphia, PA. USA. (1981).
M. J. Ablowitz, G. Biondini, S. Chakravarti, R. B. Jenkins & J. R. Sauer. “Four-wave mixing in wavelength-division-multiplexed soliton systems: damping and amplification”. Optics Letters. Vol 21, No 20, 1646–1648. (1996).
M. J. Ablowitz & G. Biondini. “Multiscale pulse dynamics in communication systems with strong dispersion management”. Optics Letters. Vol 23, No 21, 1668–1670. (1998).
M. J. Ablowitz & T. Hirooka. “Resonant nonlinear interactions in strongly dispersion-managed transmission systems”. Optics Letters. Vol 25, No 24, 1750–1752. (2000).
M. J. Ablowitz & T. Hirooka. “Nonlinear effects in quasi-linear dispersion-managed systems”. IEEE Photonics Technology Letters. Vol 13, No 10, 1082–1084. (2001).
M. J. Ablowitz, G. Biondini & E. S. Olson. “Incomplete collisions of wavelength-division multiplexed dispersion-managed solitons”. Journal of Optical Society of America B. Vol 18, No 3, 577–583. (2001).
M. J. Ablowitz & T. Hirooka. “Nonlinear effects in quasilinear dispersion-managed pulse transmission”. IEEE Journal of Photonics Technology Letters. Vol 26, 1846–1848. (2001).
M. J. Ablowitz & T. Hirooka. “Managing nonlinearity in strongly dispersion-managed optical pulse transmission”. Journal of Optical Society of America B. Vol 19, No 3, 425–439. (2002).
M. J. Ablowitz, T. Hirooka & T. Inoue. “Higher-order asymptotic analysis of dispersion-managed transmission systems: solutions and their characteristics”. Journal of Optical Society of America B. Vol 19, No 12, 2876–2885. (2002).
C. D. Ahrens, M. J. Ablowitz, A. Docherty, V. Oleg, V. Sinkin, V. Gregorian & C.R. Menyuk. “Asymptotic analysis of collision-induced timing shifts in return-to-zero quasi-linear systems with pre-and post-dispersion compensation”. Optics Letters. Vol 30, 2056–2058. (2005).
A. Biswas. “Gabitov-Turitsyn equation for solitons in multiple channels”. Journal of Electromagnetic Waves and Applications. Vol 17, No 11, 1539–1560. (2003).
A. Biswas. “Gabitov-Turitsyn equation for solitons in optical fibers”. Journal of Nonlinear Optical Physics and Materials. Vol 12, No 1, 17–37. (2003).
A. Biswas. “Dispersion-Managed solitons in multiple channels”. Journal of Nonlinear Optical Physics and Materials. Vol 13, No 1, 81–102. (2004).
A. Biswas. “Higher-order Gabitov-Turitsyn equation for dispersion-managed vector solitons in birefringent fibers”. International Journal of Theoretical Physics. Vol 46, No 12, 3339–3354. (2007).
A. Biswas. “Higher-order Gabitov-Turitsyn equation for dispersion-managed solitons”. Optik. Vol 118, No 3, 120–133. (2007).
A. Biswas & E. Zerrad. “Higher-order Gabitov-Turitsyn equation for dispersion-managed solitons in multiple channels”. International Journal of Mathematical Analysis. Vol 1, No 12, 565–582. (2007).
I. R. Gabitov & S. K. Turitsyn. “Average pulse dynamics in a cascaded transmission system with passive dispersion compensation”. Optics Letters. Vol 21, No 5, 327–329. (1996).
I. R. Gabitov & S. K. Turitsyn. “Breathing solitons in optical fiber links”. JETP Letters. Vol 63, No 10, 861–866. (1996).
T. Hirooka & A. Hasegawa. “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems”. Optics Letters. Vol 23, No 10, 768–770. (1998).
V. E. Zakharov & S. Wabnitz. Optical Solitons: Theoretical Challenges and Industrial Perspectives. Springer, Heidelberg. DE. (1999).
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Biswas, A., Milovic, D., Edwards, M. (2010). Higher Order Gabitov-Turitsyn Equations. In: Mathematical Theory of Dispersion-Managed Optical Solitons. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10220-2_9
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DOI: https://doi.org/10.1007/978-3-642-10220-2_9
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