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Solitons have been a topic of research both theoretically as well as experimentally[4] ever since their first observation was recorded by James Scott Russel in the year 1834 when he had observed a smooth shaped heap of water in a narrow canal which propagated for a few kilometers down the canal without any apparent change in its shape. However it was in the 1960’s that a mathematical model was conceived along with a corresponding solution of the non-linear equation through an inverse scattering method. Though the concept of soliton was optics based it is equally important and applicable in other areas of science like in biology, communication networks, plasma and hydrodynamics to name a few. In optics, solitons are equally important and are generally classified based on the confinement of light in space or time. The solitary wave in the former case is referred to as spatial soliton and the latter is referred to as temporal soliton[9]. A third class of spatiotemporal solitons has also been observed recently. The soliton forming phenomenon arises from the non-linear properties of the medium through which a wave is propagating. In fiber optics in concern with the soliton generation, the Kerr Effect of Self Phase Modulation[3] is of importance as it balances out with the linear effect of dispersion for soliton pulse generation. In the case of spatial soliton the natural property of light which is to disperse in space is being compensated by the nonlinearity of the medium in such a way that higher intensity part of an optical beam which is typically at the center of the employed Gaussian beam, increase a value of refractive index of medium forming

We have proposed an interesting concept of the ultra-short soliton pulse generation using microring resonators (MRRs), in which the single and multiple temporal and spatial soliton pulses could be achieved. The balance established between the dispersion and nonlinear lengths of the soliton pulse presents the soliton behavior known as self-phase modulation, which introduces the optical output constant, meaning that the light pulse can be localized coherently within the nano- waveguide. We have demonstrated that a large bandwidth of the arbitrary soliton pulses can be generated and compressed within a microring waveguide. The chaotic signal generation by means of a soliton pulse in the nonlinear MRRs has been presented. Selected light pulse can be localized and used to perform the high capacity of optical communication due to generate ultra-short bandwidth of the pulses. Localized spatial and temporal soliton pulse are useful to generate optical communication signals applicable for wired/wireless networks. As an application, the classical information and security codes can be formed by using the temporal and spatial soliton pulses, respectively.

Electrical soliton find wide uses in ultra-sharp pulse generation, nonlinear communication schemes in electronics, sharp pulse formation and edge sharpening for high speed metrology in addition to high frequency generation through Nonlinear Transmission Line (NLTL). In this paper a novel method of electrical soliton pulse generation using CMOS ring oscillator is explored. The key elements of the ring Oscillators are CMOS inverters, in which feedback is provided by a voltage divider biasing circuit. Further, by varying the feedback voltage, soliton frequency and shape analysis is done. Keywords: CMOS - ring oscillator, voltage divider bias, dark, bright electrical soliton.

A novel design of microring resonator called all-pass Mobius ring resonator is used to study optical bistability effect and spectral transmission for all-optical switching application with clockwise hysteresis loop operation. The bright soliton pulse is applied as the input source of the system. The propagation of the pulses within the system is simulated using the transfer matrix analysis. The all-pass Mobius ring resonator is able to operate under high nonlinearity as it has longer propagation length per roundtrip. The all-pass Mobius provides low transmission peak power of 3.65 mW as compared to the conventional all-pass configuration. The output-to-input relation of both design shows that the Mobius configuration is able to generate a higher hysteresis loop width of the bistable signal from 15.79 mW to 18.10 mW input power. The switching power of the optical bistability in Mobius configuration is 3.67 mW for threshold power of 16.95mW. This work shows the Mobius configuration is more suitable to be used for all-optical switching application as compared to the conventional all-pass ring resonator configuration.

Using the proposed system, we can also generate the wide range of the spread wavelength domain where the wavelength multiplexing, especially dense wavelength division multiplexing (DWDM) via optical wireless link, is probable. Moreover, the use of the quantum code distribution via an optical wireless link is confirmed by Suchat et al. [19]. However, they have proposed the system of FORR. The quantum code distribution can be generated within the MRR device. In principle, the specific wavelength mode is required in this technique, therefore, the chaotic signal is recommended to generate within the series MRRs [20]. Here the input power is in the form of Gaussian beam and expressed by Equation (2). After the Gaussian pulse is input into the first MRR device as shown in Fig.5, there are some light modes generated with smaller spectral width than the input pulse, which is obtained by the generated chaotic signals. The selected modes at the specific wavelength are required to obtain the desired use. The optical filter characteristics is employed by using the appropriate ring parameters such as input power and, ring material, refractive index, radius and coupling constant, etc. In this analysis, the Gaussian input power is 450 mW, with centre wavelength at λ 0 =1.5 µm, n 2 =2.2×10 −15 m 2 W −1 and A eff = 25 µm 2 . In Figure 5(a),

Optical soliton can be defined as a single self-reinforcing wave which is able to maintain the signal shapes while traveling with a stable speed. The Idea of optical soliton incorporates its nonlinearity feature and aims to eliminate and replace fibre optic (Ivancevic, 2010). Therefore, optical solitons are pulses that travel without distortion because of dispersion or other agents (Mishra & Konar, 2008). The subject of solitary waves is thus an important development in the field of optical communications. When located far apart, each of the solitons pulses is a wave travelling with relatively constant velocity and shape. When two pulses of optical soliton are brought together, they deform gradually and they will finally merge together creating a single wave (Solitons). However, this wave packet can be split into two discrete single waves with similar velocity and shape before they collided. Optical solitons are used in telecommunication via Wavelength Division Multiplexing (WDM) (Tripathi et al., 2007). The historical perspectives of the solitary wave are shown in Table 1.1.

Abstract: In the work, transmission of nerve impulses along nerve fibers is simulated. Research is being conducted in the framework of the electrical theory of propagation of the action potential. The soliton approach is used. The numerical experiment on the evolution of the nerve impulse and the laws of motion is conducted. It is shown that the stable form of nerve impulses solitons is realized under different initial conditions. The threshold character of occurrence of nerve pulse is simulated. It is shown that the number of pulses produced changes depending on the degree of nonlinearity: with strong initial excitation of large amplitude soliton is unstable; it breaks up into a multitude number of solitons with small ampli- tudes. In this case, the greater the nonlinearity parameter, the greater the number of births of solitons. Unusual solitonlike regimes of interaction of nonlinear pulses excitations are illustrated; in certain anomalies, colliding nerve impulses are re- flected instead of their usual quenching. The possibility of the decay of the nerve impulse at the bifurcation of the nerve fibers or the appearance of heterogeneity of the passing of a nerve impulse (the presence of dissipation in the environment) is investigated. Physical modeling allows obtaining and studying the analytical results and elucidating the physical prin- ciples of biological processes.

In this work, based on collective variable approach, we have expanded the studies of 3D dissipative pulsating solitons in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. In particular, the regions of coexistence of stationary and pulsating dissipative soliton are obtained. The collective variable approach is very efficient for approximating stable pulsating solutions when a suitable trial function is chosen. A nearly harmonic evolution of the widths along x and y axis is shown and the x and y oscillations are out of phase with the same magnitude. The dynamics of soliton can be controlled by the choice of the system parameters. So ac- cording to the values of the nonlinear gain, the system has to undergo a bifurcation from the stationary solution, to obtain pulsations with two oscillation periods. A pulsating soliton whose spectrum contains two main fre- quencies (two oscillation periods instead of one), associated to intensities of the same magnitude could also be predicted. The latter effect may be used, in principle, to grow photonic channels and multichannel arrays in bulk optical media. The collective variable technique is incomparably quicker than direct numerical computations. Of course, it should be used at the final stage of studies to confirm, complement, or invalidate the collective varia- ble approach predictions.

Wavelength selective optical add-drop filter is required for adding and dropping a particular Wavelength Division Multiplexing (WDM) channel at each subscriber node in the WDM based optical access networks. Add-drop filter used in DWDM based optical networks should have a good reflection characteristic, a temperature stability, a narrow spectral bandwidth, and a low implementation cost(Iraj Sadegh Amiri and Abdolkarim Afroozeh, 2014).For those reasons, many researchers have been proposed various technologies to generate a comb frequency of soliton using the add-drop filter(A Nikoukar et al., 2014; I. S. Amiri and J. Ali, 2014b; I. S. Amiri and J. Ali, 2014c; Y. S. Neo et al., 2014). Although add-drop filters, including those devices have good operating performances, their cost is too expensive to apply for DWDM based optical access network. The main contribution of this study is to generate multiple soliton wavelengths, train of signals or a soliton comb which is widely applicable in optical communications. MRRs are made up of waveguide by fabrication technology. Optical MRRs, filters, and switches have been successfully demonstrated in the two important GaAs-AlGaAs and GaInAsP-InP material systems (Heebner and Boyd, 1999; Hryniewicz et al., 2000). The fabrication process of the vertically coupled InP devices was developed by R. Grover (Grover et al., 2001). The III/V semiconductors (InGaAsP/InP) on the basis of InP with a direct band gap is used to fabricate the ring resonator.

These solitons are revolutionizing the telecommunication industry in leaps and bounds. Therefore it is imperative to address this NLSE model from a different perspective. This manuscript is therefore going to study the governing model with deterministic perturba- tion terms. While several journal papers are flooded with the integrability aspects of mod- els having a plethora of nonlinear optical fiber forms, the purpose of the current work is to establish a dynamical system of six soliton parameters, in presence of such determin- istic perturbations. These parameters are soliton amplitude, width, chirp, center position,

dom numbers. Then, they are converted to 32-bit IEEE floating point format [15]. The random numbers are nor- malized between [0, 1] interval to generate the number of digitization periods with selected PDF by the block la- belled as “Arithmetic IP cores”. This block performs the arithmetic floating-point operations (Equations (3) and (5)) using the dedicated hardware for high speed and ac- curate random time interval generation. A comprehensive explanation about the arithmetic operations is given in the next section. FIFO memory is necessary as a tempo- rary memory buffer for data saving because of stochastic principal of pulse generation. The generated random time interval stored in FIFO memory buffer is fetched by a written VHDL code to generate the output pulses. Relat- ed hardware and timing of the system are synchronized with the clock provided by the PLL. Average output pulse generation rate, pulse width, and PDF of each channel are adjusted by the Nios II processing core [16] through USB cable connection to the computer and its intercon- nections to different parts of the design. Figure 1 shows more information in details. The maximum working fre- quency is practically determined. It depends on the com- plexity of the architecture and the speed characteristics of the device. Detailed experimental features of the archi-

We formulate a matrix Riemann-Hilbert problem to the initial value problem for the two-component system proposed by Matsuno. By solving the asso- ciated Riemann-Hilbert problem, we can get the soliton solutions of the two-component system. One and two soliton solutions are investigated in detail.

Abstract: Optical “rogue” waves are rare and very high intensity pulses of light that occur in optical devices such as communication fibers. They appear suddenly and can cause transmission errors and damage in optical communication systems. Indeed, the physics governing their dynamics is very similar to “monster” or “freak” waves on the Earth’s oceans, which are known to harm shipping. It is therefore important to characterize rogue wave generation, dynamics and, if possible, predictability. Here we demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schrödinger equation with third-order dispersion. This generation mechanism is based on inelastic collisions of quasi- solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our theoretical and numerical results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes — a “calm before the storm” — preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of 3.865 × 10 6 ps we observe the statistics of rogue waves in optical fibres

Optical tweezer technique for molecular trapping is becoming of increasing importance for numerous biological applications. The main objective of this study was to investigate the dynamical behavior of the optical tweezers signals in microring resonators (MRR). Operating system consists of modified nonlinear add- drop optical filter made of InGaAsP/InP integrated together with a series of nonlinear nanoring resonators. This particular form is known as a PANDA ring resonator. Different models of operating system were designed and optical transfer functions for each model were derived by using Z-transform method. Simulation results were obtained from MATLAB2010a program by using parameters of practical devices. Input signals in the form of dark soliton were generated at center wavelength 1.5 µm with peak intensity 1 W/m 2 and pulse width 50 ps. Radii of rings were set to be R=34 µm, R 1 =60 nm, R 2 =60 nm, R 3 =50 nm and R 4 =50 nm respectively. Coupling

Pseudomonas aeruginosa is a common Gram-negative bacterium responsible for a wide range of infections, including those of the urinary and gastrointestinal tract, the skin, and, most prominently, the respiratory system in immunocompromised hosts and sufferers of cystic fibrosis (CF). P. aeruginosa is a well-studied opportunistic pathogen in many contexts; it is well known for its ability to form biofilms (O’Loughlin et al. 2013; Singh et al. 2015), its swarming behaviour (Daniels et al. 2004; Shrout et al. 2006), its rapid acquisition of resistance to antibiotics (Shih and Huang 2002) and its quorum sensing (QS) behaviour (Fuqua et al. 2001). QS in P. aeruginosa is of particular interest because the mechanism is more complex than the originally discov- ered, prototypical Lux homolog positive-feedback loop (e.g. James et al. 2000; Shadel and Baldwin 1991) and the number of genes regulated by QS is large (Sitnikov et al. 1995), especially those associated with virulence (O’Loughlin et al. 2013). Mathe- matical models of QS in Pseudomonas aeruginosa have received a lot of attention. They provide the formalism to summarize current understanding as well as the means to explore mechanisms and evaluate emergent solution behaviour. Here, we develop a model description, employing recent genomic information and bioinformatic tech- niques, and explore mechanisms for the generation of pulses and memory effects for downstream rhamnolipid production.

1879; Plateau, 1873). One way to create a liquid jet is by hitting a bubble with a pressure pulse. Free bubbles are often small and mobile. Therefore, they are not very suitable to obtain reproducible results in an experimental setting. The mechanism described in this report to create jets is by generating a pressure pulse at the bottom of a tube, after which the pulse moves up through a liquid column to a free surface. The words free surface and meniscus are used interchangeably. If a small, hydrophilic tube is used, then a meniscus whose surface exhibits the same shape as the lower half of a bubble will be created. These shocktube experiments are conducted to study how changes in pressure and contact angle affect the liquid jet. The results of this study can be used to improve efficiency in existing systems or to create new applications. Future applications are for example needle-free injection by generating a fast, micro-sized focused jet, or a new jet injection system in engines with a higher energy efficiency (Oudalov, 2011).

Pseudomonas aeruginosa is a common Gram-negative bacterium responsible for a wide range of infections, including those of the urinary and gastrointesti- nal tract, the skin, and, most prominently, the respiratory system in immuno- compromised hosts and sufferers of Cystic Fibrosis (CF). P. aeruginosa is a well-studied opportunistic pathogen in many contexts; it is well-known for its ability to form biofilms (O’Loughlin et al 2013; Singh et al 2015), its swarm- ing behaviour (Daniels et al 2004; Shrout et al 2006), its rapid acquisition of resistance to antibiotics (Shih and Huang 2002) and its quorum sensing (QS) behaviour (Fuqua et al 2001). QS in P. aeruginosa is of particular interest because the mechanism is more complex than the originally-discovered, pro- totypical Lux homolog positive-feedback loop (e.g., James et al 2000; Shadel and Baldwin 1991) and the number of genes regulated by QS is large (Sit- nikov et al 1995), especially those associated with virulence (O’Loughlin et al 2013). Mathematical models of QS in Pseudomonas aeruginosa have received a lot of attention. They provide the formalism to summarize current under- standing as well as the means to explore mechanisms and evaluate emergent solution behaviour. Here, we develop a model description, employing recent genomic information and bioinformatic techniques, and explore mechanisms for the generation of pulses and memory effects for downstream rhamnolipid production.

In the simulations, it is also rather straightforward to compute a time-resolved optical spectrum, i.e. the Fourier transform of the field E(x = 0, t), which is difficult in the experiment. Fig. 6a shows the spectrogram with a time window of one round-trip for the individual Fourier transforms. The WB pulse is apparent in the first 20 ns around 55 GHz. Already before the end of the address pulse, multi-mode operation sets in. At 10 ns from the beginning of the simulation, around 30 external cavity modes are present. This regime of frequency spreading is followed by a fast (around 5 ns) sweeping of the frequency spectrum towards the Bragg frequency at zero, accompanied by a narrowing to only about 15 modes. Then slower spectral evolution leads to a further narrowing of the spectrum and to the final state of the CS, which has one strong external-cavity mode slightly red detuned to the Bragg frequency with two side modes at ±5 GHz (plus some even weaker side modes). This is in accordance with the dynamics of the intensity spectra, of course. It should be noted that the survival of a single line in the field spectrum denotes cw emission whereas the presence of a single line in the intensity (RF) spectrum denotes an oscillation.

So, the goal of the present paper is (i) to build the math- ematical model of the interaction of solitary internal waves with a sill in the frame of the Navier-Stokes equations for a continuously stratified fluid, and (ii) to study in detail the dynamics of the interaction of solitary waves with a sill in or- der to answer the question of the possibility of generation of second mode solitons during such interactions: this was for- mulated as a hypothesis in the paper of H¨uttemann and Hut- ter (2001) on the basis of laboratory experiments. The paper is organised as follows. A short description of experimental data, obtained by H¨uttemann and Hutter (2001) is presented in Sect. 2. Here we describe the experimental setup of the wave channel employed and measuring technique (Sect. 2.1). Then, Sect. 2.2 presents the experimental finding of possible generation of second mode solitary waves during interaction of the first mode solitons with a sill. Section 3 is devoted to a description of the theoretical formulation of the wave process in the channel, based on the Navier-Stokes equations. Gov- erning equations, boundary conditions and numerical scheme are presented in Sect. 3.1 and then, in Sect. 3.2, the initializa- tion of the model (background fluid stratification and initial conditions) are discussed . In particular, the analytic solution of the Korteveg-de Vries equation (hereafter K-dV) for sta- tionary solitary waves in case of a smooth pycnocline is pre- sented and its use in finding the initial wave field is discussed. The results of the numerical experiments on the interaction of the internal solitary wave with a sill are presented in Sect. 4 in four parts. First, in Sect. 4.1 the basic case run with the governing parameters reproducing the laboratory experiment of Sect. 2 is described in detail. Next, the influence of the blocking parameter B (the dimensionless height of the sill), the Froude number Fr (the amplitude of the incident wave) and the viscosity are discussed in Sects. 4.2–4. A summary and conclusions are given in Sect. 5.

modern optical fiber suffers only a fraction of decibals (dB) per kilometer (km) of loss, system lengths of hundreds and thousands of kilometers will accumulate enough losses to demand the need of amplifiers. The introduction of erbium-doped fiber amplifiers (EDFAs) [3] in the early 1990s made it possible to support systems with capacity of tens and hundreds of gigabits per second (Gb/s) with an amplifier spacing of 50-100 km. Amplifiers need to be placed more frequently as system capacity increases when solitons are used since the dispersion length scales quadratically with soliton width. Thus, the demand on increasing capacity is causing the amplifier spacing to become shorter, which can drive the cost so high that the solution will become impractical. The placement of amplifier modules is therefore crucial in the design of high-capacity fiber optic systems.