Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Leadership and the negotiation of order in small groups

This thesis is focussed on the role differentiationhypothesis as it relates to small groups (Bales, 1958). The hypothesis is systematically examined, both conceptually and empirically, in the light of the Equilibrium Hypothesis (Bales, 1953) and the Negotiated Order Theory of leadership (e.g. Hosking, 1988). Chapter 1 sketches in a context for the research,which was stimulated by attempts during the 60s and 70s to organise small groups without leaders (the leaderless group, based on isocratic principles). Chapter 2 gives a conceptual and developmental overview of Bales' work, concentrating on the Equilibrium Hypothesis. It is argued that Bales' conceptual approach, if developed, can potentially integrate the disparate small groups and leadership literatures. Chapters 3 and 4 examine the concepts `group', `leader' and `leadership' in terms of the Negotiated Order perspective. In chapter 3 it is argued that two aspects of the concept group need to be taken separately into account; physical attributes and social psychological aspects (the metaphysical glue). It is further argued that a collection of people becomes a group only when they begin to establish a shared sense of social order. In chapter 4 it is argued that leadership is best viewed as a process of negotiation between those who influence and those who are influenced, in the context of shared values about means and ends. It is further argued that leadership is the process by which a shared sense of social order is established and maintained, thus linking the concepts `leadership' and `group' in a single formulation. The correspondences with Bales' approach are discussed at the end of the chapter. Chapters 5 to 8 present a detailed critical description and evaluation of the empirical work which claims to show role differentiation or test the hypothesis, both Bales original work and subsequent studies. It is argued here, that the measurement and analytical procedures adopted by Bales and others, in particular the use of simple means as summaries of group structures, are fundamentally flawed, and that role differentiation in relation to particular identifiable groups has not been demonstrated clearly anywhere in the literature. Chapters 9 to 13 present the empirical work conducted for the thesis. 18 small groups are examined systematically for evidence of role differentiation using an approach based on early sociometry (Moreno, 1934). The results suggest that role differentiation, as described by Bales, does not occur as often as is implied in the literature, and not equivocally in any case. In particular structures derived from Liking are typically distributed or weak. This suggests that one of Bales' principal findings, that Liking varies independently of his other main dimensions, is the product of statistical artifact. Chapter 14 presents a general summary of results and presents some considerations about future research.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.