Nondegenerate Solitons in Manakov System

Abstract

It is known that Manakov equation which describes wave propagation in two mode optical fibers, photorefractive materials, etc. can admit solitons which allow energy redistribution between the modes on collision that also leads to logical computing. In this paper, we point out that Manakov system can admit more general type of nondegenerate fundamental solitons corresponding to different wave numbers, which undergo collisions without any energy redistribution. The previously known class of solitons which allows energy redistribution among the modes turns out to be a special case corresponding to solitary waves with identical wave numbers in both the modes and travelling with the same velocity. We trace out the reason behind such a possibility and analyze the physical consequences. a Corresponding author E-mail: lakshman@cnld.bdu.ac.in 1 Discovery of solitons has created a new pathway to understand the wave propagation in many physical systems with nonlinearity [1]. In particular, the existence of optical solitons in nonlinear Kerr media [2] provoked the investigation on solitons from different perspectives, particularly from applications point of view. By generalizing the waves propagating in an isotropic medium[3] to an anisotropic medium, a pair of coupled equations for orthogonally polarized waves has been obtained by Manakov [4,5] aswhere q j , j = 1, 2, describe orthogonally polarized complex waves. Here the subscripts z and t represent normalized distance and retarded time, respectively. Equation (1) also appears in many physical situations such as single optical field propagation in birefringent fibers [6], self trapped incoherent light beam propagation in photorefractive medium [7-9] and so on. Generalization of Eq. (1) to arbitrary N-waves is useful to model optical pulse propagation in multi-mode fibers [10]. It has been identified [4] that the polarization vectors of the solitons change when orthogonally polarized waves nonlinearly interact with each other leading to energy exchange interaction between the modes [11]. Experimental observation of the latter has been demonstrated in [12-14]. The shape changing collision property of such waves, which we designate here as degenerate polarized soliton propagating with identical velocity and wave number in the two modes, gave rise to the possibility of constructing logic gates leading to all optical computing atleast in a theoretical sense [15-17]. Energy sharing collisions among the optical vector solitons has been explored [16]by constructing multi-soliton solutions explicitly to the multi-component nonlinear Schrödinger equations. Further, it has been shown that the multi-soliton interaction process satisfies Yang-Baxter relation [18]. It is clear from these studies that the shape changing collision that occurs among the solitons with identical wave numbers in all the modes has been well understood. However, to our knowledge, studies on solitons with non-identical wave numbers in all the modes have not been considered so far. Consequently one would like to...

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates

“…It seems that the collisions between two bound states solitons are elastic in Fig.3. Recent studies also suggested that a fundamental double-hump soliton sustains its shape even after a collision with another similar soliton [33]. However, our studies suggest that the collision between bound state solitons is usually inelastic unless the parameters satisfy the sufficient condition (19).…”

“…The profiles of the bound state soliton can be mainly classified as three different types, asymmetric doublehump soliton (for which the two components both admit asymmetric double-hump), symmetric single-humpdouble-hump soliton (for which one component admits single-hump soliton and the other component has a symmetric double-hump), and symmetric double-hump soliton (for which two components both admit symmetric double-hump). This classification is different from the one given in [33], based on different aspects for soliton profiles. The three different cases are shown in Fig.1(a1-a3), blue solid line and red dashed line corresponding to component q 1 and component q 2 respectively.…”

“…These NDBSSs can be used to investigate much richer nonlinear dynamics and interactions in multi-component BEC systems, such as beating effects, tunneling dynamics, spin-orbital coupling effects, quantum fluctuations. Note added : Recently, we noticed nondegenerate solitons were discussed in nonlinear optical fibers by the Hirota bilinear method [33]. In this paper, we perform Darboux transformation method to derive NDBSS solutions.…”

Nondegenerate soliton solutions in certain coupled nonlinear Schrödinger systems

“…Then in these cases multi-solitons moving with a single velocity have been referred as degenerate solitons. This is different from our case where we designate solitons with distinct wave numbers in different modes as nondegenerate solitons [9]. In Refs.…”

“…In contrast,, in the present context, the vector solitons already reported in the literature are designated as degenerate class of solitons. In this letter, we intend to show that the above mentioned coupled systems can admit more general class of nondegenerate soliton solutions as in the case of Manakov model reported recently by us [9] which also finds applications in multicomponent Bose-Einstein condensates [11]. Very specifically we derive such new class of soliton solutions for the two component version of CNLS equations, CCNLS equations and LSRI system one by one as we describe below.…”