Multi-soliton interactions underlying the dynamics of breather rogue waves

We consider the most famous one-breather solutions of the focusing one-dimensional nonlinear Schrodinger equation which are used in the theory of rogue waves -- the Peregrine, Akhmediev and Kuznetsov-Ma breathers, as well as the general case of drifting Tajiri-Watanabe breather. In terms of the inverse scattering transform (IST) theory, it is known that these breathers are constructed by "dressing" a plane wave solution with a single soliton. In this construction, we replace the plane wave with an exact $N$-soliton solution which converges asymptotically to the plane wave at large number of solitons $N$. As a result, we obtain exact $(N+1)$-soliton solutions practically indistinguishable from the Peregrine, Akhmediev, Kuznetsov-Ma and Tajiri-Watanabe breathers in a relatively wide region of space and time. The constructed solutions are localized in space with characteristic width proportional to $N$ and approximate the breathers with accuracy improving as $N$ grows. Our method makes it possible to build solitonic models with the same dynamical properties for the higher-order rational and super-regular breathers, and can be generalized straightforwardly to multi-breather solutions, breathers on a nontrivial background (e.g., cnoidal waves) and other integrable systems.Comment: 16 pages, 9 figure

Statistics of extreme events in integrable turbulence

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous (noise induced) modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular non-bound state gas is considered providing important insights related to the validity of the so-called virial theorem.Comment: 11 pages, 5 figure

Spatial location of correlations in a random distributed feedback Raman fiber laser

Nonlinear interactions between different components of multiwavelength radiation are one of the main processes shaping properties of quasi-CW fiber lasers. In random fiber lasers, nonlinear influence may be more complicated, as there are no distinct longitudinal modes in radiation because of the random nature of the feedback. In this Letter, we experimentally characterize internal correlations in the radiation of a multiwavelength random distributed feedback fiber laser. An analysis of Pearson correlation functions allows us to spatially locate the area over the fiber laser length in which correlations are more likely to occur. This, in turn, leads us to the conclusion about the main mechanism of spectral correlations—the relative intensity noise transfer from the pump wave

The continuous flowering gene in rose is a floral inhibitor

In rose, RoKSN, a TFL1 homologue, is a key regulator of continuous flowering. To study the function of this gene in planta, protocols of plant transformation are needed. We complemented tfl1 Arabidopsis mutants and ectopically expressed RoKSN in a continuous-flowering rose. In Arabidopsis, RoKSN complemented the tfl1 mutant by rescuing late flowering and indeterminate growth. In continuous-flowering rose, the ectopic expression of RoKSN led to the absence of flowering. In these transgenic roses, a study of genes implied in the floral regulation was carried out. The floral activator transcripts decreased whereas the FD transcription factor is up-regulated. We conclude that RoKSN is a floral repressor and could regulate the expression of transcripts as RoFT and RoFD. These results could strengthen a mechanism of competitive interactions of RoFT and RoKSN with a common partner, FD to move towards flowering or vegetative developments

Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions

RoKSN, a floral repressor, forms protein complexes with RoFD and RoFT to regulate vegetative and reproductive development in rose

FT/TFL1 family members have been known to be involved in the development and flowering in plants. In rose, RoKSN, a TFL1 homologue, is a key regulator of flowering, whose absence causes continuous flowering. Our objectives are to functionally validate RoKSN and to explore its mode of action in rose.We complemented Arabidopsis tfl1 mutants and ectopically expressed RoKSN in a continuous-flowering (CF) rose. Using different protein interaction techniques, we studied RoKSN interactions with RoFD and RoFT and possible competition. In Arabidopsis, RoKSN complemented the tfl1 mutant by rescuing late flowering and indeterminate growth. In CF roses, the ectopic expression of RoKSN led to the absence of flowering. Different branching patterns were observed and some transgenic plants had an increased number of leaflets per leaf. In these transgenic roses, floral activator transcripts decreased. Furthermore, RoKSN was able to interact both with RoFD and the floral activator, RoFT. Protein interaction experiments revealed that RoKSN and RoFT could compete with RoFD for repression and activation of blooming, respectively. We conclude that RoKSN is a floral repressor and is also involved in the vegetative development of rose. RoKSN forms a complex with RoFD and could compete with RoFT for repression of flowering

Real-time high-resolution heterodyne-based measurements of spectral dynamics in fibre lasers

Conventional tools for measurement of laser spectra (e.g. optical spectrum analysers) capture data averaged over a considerable time period. However, the generation spectrum of many laser types may involve spectral dynamics whose relatively fast time scale is determined by their cavity round trip period, calling for instrumentation featuring both high temporal and spectral resolution. Such real-time spectral characterisation becomes particularly challenging if the laser pulses are long, or they have continuous or quasi-continuous wave radiation components. Here we combine optical heterodyning with a technique of spatiooral intensity measurements that allows the characterisation of such complex sources. Fast, round-trip-resolved spectral dynamics of cavity-based systems in real-time are obtained, with temporal resolution of one cavity round trip and frequency resolution defined by its inverse (85 ns and 24 MHz respectively are demonstrated). We also show how under certain conditions for quasi-continuous wave sources, the spectral resolution could be further increased by a factor of 100 by direct extraction of phase information from the heterodyned dynamics or by using double time scales within the spectrogram approach

Optical rogue waves in coupled fiber Raman lasers

For coupled linear cavity-random fiber Raman lasers, for the first time, to the best of our knowledge, we demonstrate a new mechanism of emergence of the random pulses, with the anomalous statistics satisfying optical rogue waves’ criteria experimentally. The rogue waves appear as a result of the coupling of two Raman cascades, namely, a linear cavity laser with a wavelength of 1.55 µm and a random laser with a wavelength nearly 1.67 µm, along with coupling of the orthogonal states of polarization (SOPs). The coherent coupling of SOPs causes localization of the trajectories in the vicinity of these states, whereas polarization instability drives escape taking the form of chaotic oscillations. Antiphase dynamics in two cascades result in the suppression of low amplitude chaotic oscillations and enable the anomalous spikes, satisfying rogue waves criteria