Solution of coupled nonlinear Schrödinger equations in focusing-defocusing medium by modified perturbation theory

Jerzy Jasiński, Mirosław Karpierz


The interaction of bright solitons of different orders and two different wavelengths propagating in the medium focusing for one wavelength and defocusing for the other is considered. The system of nonlinear Schrödinger equations is solved by means of perturbation theory. Application of an additional postulate to adjust both widths of the solitons and to modify the amplitude by a factor determined by the overlap integral greatly improves the accuracy of the description. The good accuracy of description is confirmed by numerical calculations.

Full Text: PDF

  1. Y. Kivshar, G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals, (Amsterdam, Academic Press 2003). CrossRef
  2. F. Abdullaev, S. Darmanyan, P. Khabibullaev, Optical Solitons, (Springer-Verlag, Berlin, 1993) CrossRef
  3. G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE J. Selected Topics Quantum Electron. 6, (2000), 1419 CrossRef
  4. J. Yang, "Nonlinear Waves in Integrable and Nonintegrable Systems", (SIAM, Philadelphia 2010). CrossRef
  5. Y. Kivshar, B. Malomed, "Dynamics of solitons in nearly integrable systems", Rev. Mod. Phys. 61, 763 (1989). CrossRef
  6. P.G. Kevrekidis, D.J. Frantzeskakis, "Solitons in coupled nonlinear Schrödinger models: A survey of recent developments", Reviews in Physics 1 (2016), 140 CrossRef
  7. R. de la Fuente, A. Barthelemy, "Spatial soliton-induced guiding by cross-phase modulation", IEEE J. Quantum Electron. 28, 547 (1992). CrossRef
  8. H. T. Tran, R. A. Sammut, "Families of multiwavelength spatial solitons in nonlinear Kerr media", Phys. Rev. A 52, 3170 (1995). CrossRef
  9. S. Leble, B. Reichel, "Coupled nonlinear Schrödinger equations in optic fibers theory", Eur. Phys. J. Special Topics 173, 5 (2009). CrossRef
  10. M. Vijayajayanthi, T.Kanna, M. Lakshmanan, "Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities", Eur. Phys. J. Special Topics 173, 57 (2009). CrossRef
  11. S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves ", Sov. Phys. JETP 38 (1973), 248 DirectLink
  12. J. Yang, Phys. Rev. E 65, 036606 (2002). CrossRef
  13. T.Kanna, M. Lakshmanan, "Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations", Phys. Rev. Lett. 86, 5043 (2001). CrossRef
  14. M. Jakubowski, K. Steiglitz, R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media", Phys. Rev. E 58, 6752 (1998). CrossRef
  15. P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, "Supermode spatial optical solitons in liquid crystals with competing nonlinearities", Phys. Rev. A 95 (2017). CrossRef
  16. P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, and W. Krolikowski, "Supermode spatial solitons via competing nonlocal nonlinearities", Photonics Lett. Pol. 10 (2018). CrossRef
  17. A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto, "Scalar and vector supermode solitons owing to competing nonlocal nonlinearities", Opt. Express 29, 8015 (2021) CrossRef

Full Text:


We use cookies that are necessary for the website to function and cannot be switched off in our systems. Click here for more information.

Photonics Letters of Poland - A Publication of the Photonics Society of Poland
Published in cooperation with SPIE

ISSN: 2080-2242