Rogue Solitons Research Articles

Generation and controlling of ultrashort self-similar solitons and rogue waves in inhomogeneous optical waveguide

We present exact bright, dark and rogue soliton solutions of generalized higher-order nonlinear Schrödinger equation, describing the ultrashort beam propagation in tapered waveguide amplifier, via a similarity transformation connected with the constant-coefficient Sasa–Satsuma and Hirota equations. Our exact analysis takes recourse to identify the allowed tapering profile in conjunction with appropriate gain function which corresponds to PT-symmetric waveguide. We extend our analysis to study the effect of tapering profiles and higher-order terms on the evolution of self-similar waves and thus enabling one to control the self-similar wave structure and dynamical behavior.

Machine learning analysis of rogue solitons in supercontinuum generation

Supercontinuum generation is a highly nonlinear process that exhibits unstable and chaotic characteristics when developing from long pump pulses injected into the anomalous dispersion regime of an optical fiber. A particular feature associated with this regime is the long-tailed “rogue wave”-like statistics of the spectral intensity on the long-wavelength edge of the supercontinuum, linked to the generation of a small number of “rogue solitons” with extreme red-shifts. Whilst the statistical properties of rogue solitons can be conveniently measured in the spectral domain using the real-time dispersive Fourier transform technique, we cannot use this technique to determine any corresponding temporal properties since it only records the spectral intensity and one loses information about the spectral phase. And direct temporal characterization using methods such as the time-lens has resolution of typically 100’s of fs, precluding the measurement of solitons which possess typically much shorter durations. Here, we solve this problem by using machine learning. Specifically, we show how supervised learning can train a neural network to predict the peak power, duration, and temporal walk-off with respect to the pump pulse position of solitons at the edge of a supercontinuum spectrum from only the supercontinuum spectral intensity without phase information. Remarkably, the network accurately predicts soliton characteristics for a wide range of scenarios, from the onset of spectral broadening dominated by pure modulation instability to near octave-spanning supercontinuum with distinct rogue solitons.

Semi-rational and periodic wave solutions for the (3+1)-dimensional Jimbo–Miwa equation

In this paper, higher-order periodic wave solution in determinant form is investigated via the Kadomtsev–Petviashvili hierarchy reduction for the $$(3+1)$$-dimensional Jimbo–Miwa equation. We obtain the breather and periodic wave via such solution. The breather is periodic in space and localized in time, while amplitude of the periodic wave changes with the value of y. Besides, interaction between the breather and periodic wave shows a different characteristic in which amplitude of the periodic wave changes after the interaction. By taking the long wave limit to the periodic wave solution, we obtain the semi-rational solution, and then derive the rogue wave and kink-like soliton. Furthermore, we conclude that (1) rogue wave can be obtained with the limit on the breather; (2) kink-like soliton can be obtained with the limit on the periodic wave. Via the semi-rational solution, interactions between the rogue wave and breather, between the kink-like soliton and breather, are illustrated.

LUMP AND MIXED ROGUE-SOLITON SOLUTIONS TO THE 2+1 DIMENSIONAL ABLOWITZ-KAUP-NEWELL-SEGUR EQUATION

In this paper, the 2+1 dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation which obtained from the potential Boiti-Leon-Manna-Pempi nelli (pBLMP) equation, is introduced. Through the bilinear method and ansatz technique, the rational solutions consisting of rogue wave and lump soliton solutions are constructed, where we discuss the condition of guaranteeing the positiveness and analyticity of the lump solutions. The collection of a quadratic function with an exponential function describing rationalexponential solutions is proved, the interaction consisting of one lump and one soliton with fission and fusion phenomena. The second kind of interaction comprises the line rogue wave and soliton solution, which is inelastic. With the usage of the extended homoclinic test approach, the homoclinic breather-wave solution is derived. The characteristics of these various solutions are exhibited and illustrated graphically.

A train of bright and dark-rogue wave solitons in a polariton fluid with inhomogeneous strength interaction

We solve using the similarity transformation method a one-dimensionless driven-dissipative nonlinear Schrodinger equation to explore the dynamics of the rogue wave solitons generated in a polariton fluid. Under resonant excitation, we predict the existence of the bright and the dark-rogue waves solitons by varying the external pump source parameter. By considering, a time periodic polariton–polariton interaction and adjusting its frequency, the rogue wave soliton trains occur in a polariton fluid. In addition we observe that, the amplitude of the pump power is responsible to the formation of a the train of the bright and the dark rogue waves solitons.

Rogue waves and lump solitons for a -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation is a -dimensional B-type Kadomtsev–Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, , increasing when . In addition, dark rogue waves are derived when . Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter , and amplitude of the lump soliton is negatively correlated with when .

Supercontinuum and rogue soliton generation by induced modulational instability in photonic crystal fibre

We present an approach that enables active control of supercontinuum (SC) and rogue soliton (RS) generation through the modulation of a 500 fs input pulse by numerical simulations. The induced modulational instability contributes to the initial comb-like SC generation, which is fundamentally different from SC initiated by high-order soliton fission. The output spectrum shows great dependence on modulation frequencies and depths. It is interesting that we can manipulate the RS generation by adjusting the modulation parameters. And we also demonstrate the conditions which can be beneficial to RS generation: (i) very weak or large values of modulation depth; (ii) seeding in the vicinity of the peak of the modulational instability gain spectrum. Although RS degrades the smoothness of the SC, it is of great significance in the generation of tailored SC.

Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

We have investigated the ()-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.

Rogue waves and breathers in Heisenberg spin chain

Following the connection of the non-linear Schrodinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.

Rogue solitons in optical fibers: a dynamical process in a complex energy landscape?

Nondeterministic giant waves, denoted as rogue, killer, monster, or freak waves, have been reported in many different branches of physics. Their physical interpretation is however still debated: despite massive numerical and experimental evidence, a solid explanation for their spontaneous formation has not been identified yet. Here we propose that rogue waves [more precisely, rogue solitons (RSs)] in optical fibers may actually result from a complex dynamical process very similar to well-known mechanisms such as glass transitions and protein folding. We describe how the interaction among optical solitons produces an energy landscape in a highly dimensional parameter space with multiple quasi-equilibrium points. These configurations have the same statistical distribution of the observed rogue events and are explored during the light dynamics due to soliton collisions, with inelastic mechanisms enhancing the process. Slightly different initial conditions lead to very different dynamics in this complex geometry; a RS turns out to stem from one particularly deep quasi-equilibrium point of the energy landscape in which the system may be transiently trapped during evolution. This explanation will prove to be fruitful to the vast community interested in freak waves.

Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation

We numerically study the impacts of introducing a minute continuous-wave (CW) trigger on the properties of picosecond supercontinuum (SC) generation. We show that this simple triggering approach enables active control of not only the bandwidth, but more importantly the temporal coherence of SC. Detailed numerical simulations suggest that depending on the wavelength of the CW-trigger the multiple higher-order four-wave mixing (FWM) components generated by the CW-trigger can create either a relatively more stochastic or a more deterministic beating effect on the pump pulse, which has significant implications on how soliton fission and the onset of SC are initiated in the presence of noise. By controlling the CW-trigger wavelengths, the rogue solitons emerged in SC generation can exhibit high-degree of temporal coherence and pulse-to-pulse intensity stability. The present study provides a valuable insight on how the initial soliton fission can be initiated in a more controllable manner such that SC generation with both high temporal coherence and stability can be realized.

Collisions and turbulence in optical rogue wave formation

We discuss optical rogue wave generation in terms of collisions and turbulence processes. Simulations of picosecond pulse propagation in optical fibres show rogue soliton generation from either third-order dispersion or Raman scattering independently. Simulations of rogue soliton emergence with dispersive perturbation in the long-distance limit are also presented.