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Infantologies II is a continuation of a series of articles that began with the quartet: Infantologies, Infanticides, Infantasies, Infantilizations. ‘Infantologies II: Songs of the Cradle’ is devoted to fairy stories, nursery rhymes and the poetics of early childhood. Each author engages with these themes through different questions and contexts, contributing their thoughts on the complexity of the fairy stories, nursery rhymes and the poetics of early childhood to the infantology collection.

Periodic structures may grow in both conservative and dissipative systems. A multiplicity of examples can be found in nature and in the laboratory. However, periodic structures may grow and decay. We show that the effects of dissipation are essential for these structures to remain. Using the nonlinear Schrödinger equation and its extensions as basic examples of conservative and dissipative systems we show that there are two ways of adiabatic transformations of a continuous-wave solution into a train of pulses.

Dissipative solitons with extreme spikes (DSESs), previously thought to be rare solutions of the complex cubic- quintic Ginzburg-Landau equation, occupy in fact a significant region in its parameter space. The variation of any of its five parameters results in a rich structure of bifurcations. We have constructed several bifurcation diagrams that reveal periodic and chaotic dynamics of DSESs. There are various routes to the chaotic behavior of DSESs, including a sequence of period-doubling bifurcations. It is well known that the complex cubic-quintic Ginzburg-Landau equation can serve as a master equation for the description of passively mode-locked lasers. Our results may lead to the observation of DSESs in laser systems.

Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect.

Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect. © 2016 American Physical Society

Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states >breather turbulence> or >soliton turbulence.> The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics. ©2016 American Physical Society

We study the properties of the chaotic wave fields generated in the frame of the Sasa- Satsuma equation when a plane wave solution is randomly perturbed with a white noise. We have found that plane waves with different propagation constant splits into selffocused filaments, that propagate with a velocity which is well approximately given by the group velocity calculated from the dispersion relation for the plane wave solution. Different propagation constants are considered and a good agreement is obtained with the numerical solution. We have also calculated the density of probability of having a wave of given amplitude, therefore determining the probability of appearance of rogue waves. Their spectra are also analized.

We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation, and analyze the presence of rogue waves in them. Our results also reveal the reason for the skewed profile of the exact rogue wave solutions.

© 2014 American Physical Society. We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter - the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

© 2014 Elsevier B.V. All rights reserved. We analyze the rogue wave spectra of the Sasa-Satsuma equation and their appearance in the spectra of chaotic wave fields produced through modulation instability. Chaotic wave fields occasionally produce high peaks that result in a wide triangular spectrum, which could be used for rogue wave detection.

We study, numerically, the influence of third-order dispersion (TOD) on modulation instability (MI) in optical fibers described by the extended nonlinear Schrödinger equation. We consider two MI scenarios. One starts with a continuous wave (CW) with a small amount of white noise, while the second one starts with a CW with a small harmonic perturbation at the highest value of the growth rate. In each case, the MI spectra show an additional spectral feature that is caused by Cherenkov radiation. We give an analytic expression for its frequency. Taking a single frequency of modulation instead of a noisy CW leads to the Fermi-Pasta-Ulam (FPU) recurrence dynamics. In this case, the radiation spectral feature multiplies due to the four-wave mixing process. FPU recurrence dynamics is quite pronounced at small values of TOD, disappears at intermediate values, and is restored again at high TOD when the Cherenkov frequency enters the MI band. Our results may lead to a better understanding of the role of TOD in optical fibers. © 2012 Optical Society of America.

The ability to unveil growing rogue waves in the ocean is essential for safe marine travel in stormy conditions. This vital problem has not been adequately addressed so far. We show that the specific triangular spectra of rogue waves can be detected at early stages of their development in a chaotic wave field. Continuously measuring the spectra of various parts of the wave field allows us to find a rogue wave before the dangerous peak appears. This possibility of early detection is a necessary part of a rogue wave early-warning system.

The ghosts of this paper refer to the ways in which diverse practices and learning styles coincide in particular frames. This article will combine the philosophy of mind with educational poststructuralism to generate an informed approach to understand learning-practice. This combinational analysis rests on certain principles and focus points such as: 1) Language plays a crucial role in the orchestration of practice; 2) Learning cannot be separated from its contextual instantiations; 3) The conjunction learning-practice is meaningless without a discussion about the language of practice and the learning context. This approach called learning-practice will be furnished with an example taken from research into vocational education and the learning of an orchestra. This example will act as an experimental field to test the principles and focus points of learning-practice. The research field also acts to examine the coherence and cogency of the philosophy of education that we may draw from this perspective that strategically deploys ideas taken from Ludwig Wittgenstein, Gilles Deleuze & Félix Guattari and Gilbert Ryle.

We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring. © 2009 Optical Society of America.

Dissipative media admit the existence of two types of stationary self-organized beams: continuously self-focused and continuously self-defocused. Each beam is stable inside of a certain region of its existence. Beyond these two regions, beams loose their stability, and new dynamical behaviors appear. We present several types of instabilities related to each beam configuration and give examples of beam dynamics in the areas adjacent to the two regions. We observed that, in one case beams loose the radial symmetry while in the other one the radial symmetry is conserved during complicated beam transformations. © 2008 Optical Society of America.

Using the Lagrangian formalism, with a simple trial function for dissipative optical two-dimensional (2D) soliton beams, we show that there are two disjoint sets of stationary soliton solutions of the complex cubic-quintic Ginzburg-Landau equation, with concave and convex phase profiles, respectively. These correspond to continuously self-focusing and continuously self-defocusing types of 2D solitons. Their characteristics are distinctly different, as the energy for their existence can be generated either at the center or in the outer layers of the soliton beam. These predictions are corroborated with direct numerical simulations of the Ginzburg-Landau equation. Regions of existence in the parameter space of these two types of solutions are found and they are in reasonable agreement with the predictions of the Lagrangian approach. In addition, direct numerical simulations allow us to find more complicated localized solutions around these regions. These solutions lack cylindrical symmetry and/or pulsate in time. Examples of the complex behavior of these beams are presented. © 2008 The American Physical Society.

How do we understand our own cultural histories and how do these understandings impact on our senses of self? This paper addresses the case of Pacific islander migration into New Zealand. It is based on a study fuelled by a group of Pacific island teachers exploring their own experiences of becoming teachers in New Zealand schools. The paper raises some theoretical issues relating to cultural identity as understood in relation to educational practices at the interfaces of cultures. By examining how notions of Pacific cultural identity for individuals are held in place by particular self-images the paper asks how such identities might be seen as reaching out to possible futures. The paper concludes with some tentative thoughts on how an individual might work towards strengthening a historical sense of self and a more productive reflective/reflexive conception of engagement in a situation of cultural minority.

Using the method of moments for dissipative optical solitons, we show that there are two disjoint sets of fixed points. These correspond to stationary solitons of the complex cubic-quintic Ginzburg-Landau equation with concave and convex phase profiles respectively. Numerical simulations confirm the predictions of the method of moments for the existence of two types of solutions which we call solitons and antisolitons. Their characteristics are distinctly different. © 2007 Elsevier B.V. All rights reserved.