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...

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In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schrödinger type equations through bilinearization procedure. In particular, we consider coupled nonlinear Schrödinger (CNLS) equations (both focusing as well as mixed type nonlinearities), coherently coupled nonlinear Schrödinger (CCNLS) equations and long-wave-short-wave resonance interaction (LSRI) system. We point out that the obtained general form of soliton solutions exhibit novel profile structures than the previously known degenerate soliton solutions corresponding to identical wave numbers in both the modes. We show that such degenerate soliton solutions can be recovered from the newly derived nondegenerate soliton solutions as limiting cases.

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the coupled nonlinear Schrödinger (CNLS) family of equations. In the recent past, many types of vector solitons have been identified both in the integrable and non-integrable CNLS framework. In this article, we review some of the recent progress in understanding the dynamics of the so called nondegenerate vector bright solitons in nonlinear optics, where the fundamental soliton can have more than one propagation constant. We address this theme by considering the integrable two coupled nonlinear Schrödinger family of equations, namely the Manakov system, mixed 2-CNLS system (or focusing-defocusing CNLS system), coherently coupled nonlinear Schrödinger (CCNLS) system, generalized coupled nonlinear Schrödinger (GCNLS) system and two-component long-wave short-wave resonance interaction (LSRI) system. In these models, we discuss the existence of nondegenerate vector solitons and their associated novel multi-hump geometrical profile nature by deriving their analytical forms through the Hirota bilinear method. Then we reveal the novel collision properties of the nondegenerate solitons in the Manakov system as an example. The asymptotic analysis shows that the nondegenerate solitons, in general, undergo three types of elastic collisions without any energy redistribution among the modes. Furthermore, we show that the energy sharing collision exhibiting vector solitons arises as a special case of the newly reported nondegenerate vector solitons. Finally, we point out the possible further developments in this subject and potential applications.

In this letter we report the existence of nondegenerate fundamental bright soliton solution for coupled multi-component nonlinear Schrödinger equations of Manakov type. To derive this class of nondegenerate vector soliton solutions, we adopt the Hirota bilinear method with appropriate general class of seed solutions. Very interestingly the obtained nondegenerate fundamental soliton solution of the N-coupled nonlinear Schrödinger (CNLS) system admits multi-hump natured intensity profiles. We explicitly demonstrate this specific property by considering the nondegenerate soliton (NDS) solutions for 3 and 4-CNLS systems. We also point out the existence of a special class of partially NDS solutions by imposing appropriate restrictions on the wavenumbers in the already obtained completely NDS solution. Such class of soliton solutions can also exhibit multi-hump profile structures. Finally, we present the stability analysis of nondegenerate fundamental soliton of the 3-CNLS system as an example. The numerical results confirm the stability of triple-humped profile nature against perturbations of 5% and 10% white noise. The multi-hump nature of nondegenerate fundamental soliton solution will be useful in multi-level optical communication applications with enhanced flow of data in multi-mode fibers.

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