Abstract
It is well known that solitons in integrable systems recover their original profiles after their mutual collisions. This is not true in the case of optical fibre arrays, governed by a set of integrable coupled nonlinear Schrödinger (CNLS) equations. We consider the Manakov- and mixed-type ‘two-component’ CNLS systems. The most important characteristics of these systems are: (1) The polarizations of the two-component solitons are changed through their mutual collisions (Manakov system) and (2) the energy (intensity) switching occurs through the head-on collision (mixed system). By placing the above solitons on the primary star graph (PSG), we see that soliton collisions give rise to interesting phase changes in PSG: (a) The transition in PSG from its depolarized state to polarized one; (b) a state with selectively amplified bond is generated on PSG from its homogeneous state. These results will be applicable to network protocols using optical fibre arrays.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y S Kivshar and G P Agrawal, Optical solitons: From fibres to photonic crystals (Academic, San Diego, 2003)
L F Mollenauer and J P Gordon, Solitons in optical fibres: Fundamentals and applications (Academic, San Diego, 2006)
R Radhakrishnan, M Lakshmanan and J Hietarinta, Phys. Rev. E 56, 2213 (1997)
T Kanna and M Lakshmanan, Phys. Rev. Lett. 86, 5043 (2001)
T Kanna, M Lakshmanan, P T Dinda and N Akhmediev, Phys. Rev. E 73, 026604 (2006)
M H Jakubowski, K Steiglitz and R Squier, Phys. Rev. E 58, 6752 (1998)
K Steiglitz, Phys. Rev. E 63, 016608 (2000)
I Kaminer, M Segev, A M Bruckstein and Y C Eldar, Proc. R. Soc. A 465, 1093 (2009)
S Flach and C R Willis, Phys. Rep. 295, 181 (1998)
R Burioni, D Cassi, P Sodano, A Trombettoni and A Vezzani, Chaos 15, 043501 (2005); Physica D 216, 71 (2006)
A S Pikovsky and D L Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008)
G Kopidakis, S Komineas, S Flach and S Aubry, Phys. Rev. Lett. 100, 084103 (2008)
M J Ablowitz and H Segur, J. Math. Phys. 16, 1054 (1975)
A S Fokas, A R Its and L-Y Sung, Nonlinearity 18, 1771 (2005)
J I Ramos and F R Villatoro, Math. Comput. Modelling 20, 31 (1994)
A S Fokas and A R Its, J. Phys. A: Math. Gen. 37, 6091 (2004)
C Sulem and P L Sulem, The nonlinear Schrödinger equation (Springer, New York, 1999)
M J Ablowitz, B Prinari and A D Trubatch, Discrete and continuous nonlinear Schrödinger systems (Cambridge University Press, Cambridge, 2004)
Z Sobirov, D Matrasulov, K Sabirov, S Sawada and K Nakamura, Phys. Rev. E 81, 066602 (2010)
K Nakamura, Z A Sobirov, D U Matrasulov and S Sawada, Phys. Rev. E 84, 026609 (2011)
V E Zakharov and A B Shabat, Sov. Phys. JETP 34, 62 (1972)
R Hirota, The direct method in soliton theory (Cambridge University Press, Cambridge, 2004)
in preparation
Acknowledgements
KN is grateful to Prof. M Lakshmanan for invitation to Bharathidasan University in Tiruchirappalli in February 2014, which has made possible the present work. TK and KS thank the Principal and management of Bishop Heber College for constant support and encouragement. KS acknowledges the support of Council of Scientific and Industrial Research, Government of India, in the form of Senior Research Fellowship.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nakamura, K., Kanna, T. & Sakkaravarthi, K. Protocol of networks using energy sharing collisions of bright solitons. Pramana - J Phys 85, 1009–1021 (2015). https://doi.org/10.1007/s12043-015-1112-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-015-1112-7