https://doi.org/10.1140/epjd/e2010-00162-0
Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations from the birefringent optical fibers
1
School of Science, P.O. Box 122, Beijing University of
Posts and Telecommunications, Beijing, 100876, China
2
State Key Laboratory of Software Development Environment, Beijing
University of Aeronautics and Astronautics, Beijing, 100191, China
3
Key Laboratory of Information Photonics and Optical
Communications (BUPT), Ministry of Education, P.O. Box 128,
Beijing University of Posts and Telecommunications, Beijing, 100876, China
Corresponding author: a tian.bupt@yahoo.com.cn
Received:
25
February
2010
Revised:
21
April
2010
Published online:
11
June
2010
Coupled modified nonlinear Schrödinger (CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. A new type of the Lax pair and another hierarchy of the infinitely many conservation laws are derived based on the Wadati-Konno-Ichikawa system. By means of the Hirota method, soliton solutions in the normal dispersion regime are obtained. Parametric regions for the existence of dark and anti-dark vector soliton solutions are given. Asymptotic analysis shows that the collision between two solitons (two anti-dark solitons, two dark solitons, or dark and anti-dark solitons) in each polarization direction is elastic. Moreover, there is no energy transfer between two polarization components of each vector soliton, whether dark or anti-dark vector soliton. In addition, dark and anti-dark solitons can coexist on the same background seen from the collision between the dark and anti-dark solitons in one polarization direction. Our graphical analysis shows that the parameters in the CMNLS equations not only determine the regions for the existence of dark and anti-dark soliton solutions but also control the phase and direction of the propagation of the solitons. Finally, through the linear stability analysis, the modulational instability condition is given.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010
