Abstract—The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system. Keywords—Optical soliton, soliton interaction, soliton switching, WDM. I. INTRODUCTION N the context of optical fiber communications and nonlinear optics, nonlinear Schrödinger equations have been employed to describe the optical pulse propagation in nonlinear optical fiber. Since the theoretical prediction [1] and experimental observation [2], optical solitons has potential applications in the optical communication. Optical solitons ascend when the linear dispersion and nonlinear effects are exactly balanced. Optical soliton propagation in single-mode fibers is governed by the nonlinear Schrödinger (NLS) equation, which involves the GVD and self-phase modulation (SPM) [3]. However, single-mode optical fibers are not really “single-mode” but are actually bimodal because of the birefringence induced by various imperfections randomly distributed along the fiber [4]. In the picosecond regime, the governing model for the vector solitons propagation in the birefringent fibers is the coupled nonlinear Schrödinger (CNLS) system [5]. Actual observations suggest that the core medium in a real fiber is not homogeneous due to some nonuniformity factors such as the variation in the lattice parameters of the fiber and fluctuation of the fiber geometry [6]. One of the most exciting phenomena associated with solitons is their collisions. It is well known that if the solitons interact like particles cross each other unaffectedly only by a phase shift, then the collision is elastic. In addition, the physical quantities such as amplitudes S. Arun Prakash and V.Malathy are with the Electrical Department, Anna University, Madurai Region, Ramanathapuram 623513, Tamilnadu, India (phone: 9790328649, +91 9894068686; e-mail: arunprakashmadurai@ gmail.com vmeee@autmdu.ac.in). M. S. Mani Rajan is with the Physics Department, Anna University, Ramanathapuram 623513, Tamilnadu, India (phone: +91 9940740238; e-mail: senthilmanirajanofc@ gmail.com). and velocities are conserved. In particular, optical solitons, which exhibit the fascinating characteristics of self-guided beams, are an attractive and active area of research, because of their potential applications in many areas, including all optical switching, optical data storage, design of logic gates, and processing. To enhance the communication quality of high-bit rate and long-distance optical communication systems, soliton interaction based on the NLS-typed equations have been worked out [7], [8]. Recently, soliton collision in CNLS system has been investigated by [9]. Very recently, soliton interaction in CNLS equation with higher order effects has been performed in [10]. II. MODEL To investigate this case we consider 3-CNLSE with variable coefficients as: 0 ) ( ) ( ) ( 2 ) ( 0 ) ( ) ( ) ( 2 ) ( 0 ) ( ) ( ) ( 2 ) ( 3 3 3 2 2 2 1 3 3 2 2 3 2 2 2 1 2 2 1 1 3 2 2 2 1 1 1 = + + + + + = + + + + + = + + + + + q z i q q q q z q z q i q z i q q q q z q z q i q z i q q q q z q z q i tt z tt z tt z δ γ β δ γ β δ γ β (1) where q 1 , q 2 and q 3 are slowly varying envelopes of three optical modes, the variables z and t, respectively, correspond to the propagation distance and time. β (z), ) (z γ , ) ( z δ are the variable coefficients which are associated with group velocity dispersion (GVD), nonlinearity and fiber loss/ gain, respectively. In practical applications, the model is of primary interest not only for the dispersion and for nonlinear management of a soliton in inhomogeneous systems, but also to examine the soliton propagation in wavelength division multiplexing (WDM) system. III. LAX PAIR In this section, with symbolic computation, we will construct the Lax pair of (1) via the Ablowitz–Kaup–Newell– Segur scheme (AKNS) [11]. From the Lax pair, multi soliton solutions can be generated effectively by means of Darboux transformation. 1 2 3 ; ; ( , , ) t z T U V ψ ψ ψ ψ ψ ϕϕϕ = = = P J i U + = , Q P J i V + + = λ λ 2 2 Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System S. Arun Prakash, V. Malathi, M. S. Mani Rajan I World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:9, No:12, 2015 714 International Scholarly and Scientific Research & Innovation 9(12) 2015 scholar.waset.org/1307-6892/10002966 International Science Index, Physical and Mathematical Sciences Vol:9, No:12, 2015 waset.org/Publication/10002966