Research PapersNo Access

Bound-state solutions, Lax pair and conservation laws for the coupled higher-order nonlinear Schrödinger equations in the birefringent or two-mode fiber

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Search for more papers by this author

Bo Tian

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

E-mail Address: tian_bupt@163.com

Corresponding author.

Search for more papers by this author

, and

Xi-Yang Xie

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Search for more papers by this author

https://doi.org/10.1142/S0217984917500671Cited by:20 (Source: Crossref)

Abstract

For describing the propagation of ultrashort pulses in the birefringent or two-mode fiber, we consider the coupled nonlinear Schrödinger equations with higher-order effects. According to the Ablowitz–Kaup–Newell–Segur system, 3 $\times$ 3 Lax pair for such equations is derived. Based on the Lax pair, we construct the conservation laws and Darboux transformation (DT). One- and two-soliton solutions are obtained via the DT, and we graphically present the one soliton and bound-state two solitons.

Keywords:

References

1. C. Kharif, E. Pelinovsky and A. Slunyaev, Rogue Waves in the Ocean (Springer, Heidelberg, 2009). Google Scholar
2. N. Akhmediev, A. Ankiewicz and M. Taki, Phys. Lett. A 373 (2009) 675. Crossref, Web of Science, ADS, Google Scholar
3. K. Dysthe, H. E. Krogstad and P. Müller, Annu. Rev. Fluid Mech. 40 (2008) 287. Crossref, Web of Science, ADS, Google Scholar
4. Z. P. Yang, W. P. Zhong and M. Belić, Laser Phys. 25 (2015) 085402. Crossref, Web of Science, Google Scholar
5. L. Wang, J. H. Zhang, Z. Q. Wang, C. Liu, M. Li, F. H. Qi and R. Guo, Phys. Rev. E 93 (2016) 012214. Crossref, Web of Science, ADS, Google Scholar
6. J. J. Su, Y. T. Gao and S. L. Jia, Commun. Nonlinear Sci. Numer. Simul. 50 (2017) 128. Crossref, Web of Science, ADS, Google Scholar
7. J. M. Dudley, F. Dias, M. Erkintalo and G. Genty, Nat. Photonics 8 (2014) 755. Crossref, Web of Science, ADS, Google Scholar
8. J. W. Yang, Y. T. Gao, C. Q. Su, D. W. Zuo and Y. J. Feng, Commun. Nonlinear Sci. Numer. Simulat. 42 (2017) 477. Crossref, Web of Science, ADS, Google Scholar
9. J. J. Su and Y. T. Gao, Eur. Phys. J. Plus 132 (2017) 53. Crossref, Web of Science, Google Scholar
10. F. H. Qi, X. G. Xu and P. Wang, Appl. Math. Lett. 54 (2016) 60. Crossref, Web of Science, Google Scholar
11. J. W. Yang, Y. T. Gao, Y. J. Feng and C. Q. Su, Nonlinear Dynam. 87 (2017) 851. Crossref, Web of Science, Google Scholar
12. Y. V. Bludov, V. V. Konotop and N. Akhmediev, Phys. Rev. A 80 (2010) 033610. Crossref, Web of Science, Google Scholar
13. H. Bailung, S. K. Sharma and Y. Nakamura, Phys. Rev. Lett. 107 (2011) 255005. Crossref, Web of Science, ADS, Google Scholar
14. M. Lakshmanan, K. Porsezian and M. Daniel, Phys. Lett. A 133 (1988) 483. Crossref, Web of Science, ADS, Google Scholar
15. T. A. Davydova and Y. A. Zaliznyak, Physica D 156 (2001) 260. Crossref, Web of Science, ADS, Google Scholar
16. A. Hasegawa, Opt. Lett. 5 (1980) 416. Crossref, Web of Science, ADS, Google Scholar
17. W. R. Sun, B. Tian, Y. F. Wang and H. L. Zhen, Opt. Commun. 335 (2015) 237. Crossref, Web of Science, ADS, Google Scholar
18. Q. M. Huang, Y. T. Gao, S. L. Jia, Y. L. Wang and G. F. Deng, Nonlinear Dynam. 87 (2017) 2529; Z. Z. Lan, Y. T. Gao, J. W. Yang, C. Q. Su and B. Q. Mao, Commun. Nonlinear Sci. Numer. Simulat. 44 (2017) 360; Z. Z. Lan, Y. T. Gao, J. W. Yang, C. Q. Su and Q. M. Wang, Mod. Phys. Lett. B 30 (2016) 1650265; X. Y. Gao, Ocean Engineering 96 (2015) 245; X. Y. Gao, Mod. Phys. Lett. B 30 (2016) 1650217; P. Jin, C. A. Bouman and K. D. Sauer, IEEE Trans. Comput. Imaging 1 (2015) 200. Google Scholar
19. M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Phys. Rev. Lett. 31 (1973) 125. Crossref, Web of Science, ADS, Google Scholar
20. K. Konno, H. Sanuki and Y. H. Ichikawa, Prog. Theor. Phys. 52 (1974) 3. Crossref, Google Scholar
21. H. Sanuki and K. Konno, Phys. Lett. A 48 (1974) 221. Crossref, Web of Science, ADS, Google Scholar
22. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991). Crossref, Google Scholar
23. T. A. Davydova and Y. A. Zaliznyak, Physica D 156 (2001) 260. Crossref, Web of Science, ADS, Google Scholar
24. S. L. Palacios, J. M. Fernandez-Diaz, Opt. Commun. 178 (2000) 457. Crossref, Web of Science, ADS, Google Scholar
25. P. D. Lax, Comm. Pure Appl. Math. 21 (1968) 467. Crossref, Web of Science, Google Scholar
26. M. J. Ablowitz and P. A. Clarkson, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1992). Crossref, Google Scholar