Peregrine soliton generation and breakup in standard telecommunications fiber

We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of nonideal initial conditions is studied through direct cutback measurements of the longitudinal evolution of the emerging soliton dynamics and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.     

非线性色散渐减光纤中高峰值脉冲的激发和传输

本文基于变系数的非线性薛定谔方程,数值地讨论高峰值脉冲在色散渐减光纤中的激发和传输。首先,基于变系数非线性薛定谔方程的Peregrine孤子解,解析和数值地讨论精确的Peregrine孤子在色散渐减光纤中的传输特性。其次,通过输入不同的平面波背景上的局域脉冲,研究高峰值脉冲在非线性色散渐减光纤中的激发和传输。结果显示Peregrine孤子在色散渐减光纤中传输时,会产生一个空间和时间都局域化的高峰值单脉冲,并且当啁啾为负时,脉冲的幅值增加,脉宽被压缩。若光纤系统存在增益,脉冲的幅值也会增加。由于非线性光纤中的调制不稳定性过程,不同平面波背景上的小局部扰动都可激发出高峰值脉冲,除了峰值和宽度略有不同外,激发脉冲的形状几乎相同。     

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.     

Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems

In the present work, we examine the potential robustness of extreme wave events associated with large amplitude fluctuations of the Peregrine soliton type, upon departure from the integrable analogue of the discrete nonlinear Schrödinger (DNLS) equation, namely the Ablowitz–Ladik (AL) model. Our model of choice will be the so-called Salerno model, which interpolates between the AL and the DNLS models. We find that rogue wave events are drastically distorted even for very slight perturbations of the homotopic parameter connecting the two models off of the integrable limit. Our results suggest that the Peregrine soliton structure is a rather sensitive feature of the integrable limit, which may not persist under “generic” perturbations of the limiting integrable case.     

Rogue waves management by external potentials

We study the effect of time-dependent linear and quadratic potentials on the profile and dynamics of rogue waves represented by a Peregrine soliton. The Akhmediev breather, Ma breather, bright soliton, Peregrine soliton, and constant wave (CW) are all obtained by changing the value of one parameter in the general solution corresponding to the amplitude of the input CW. The corresponding solutions for the case with linear and quadratic potentials were derived by the similarity transformation method. While the peak height and width of the rogue wave turn out to be insensitive to the linear potential, the trajectory of its center-of-mass can be manipulated with an arbitrary time-dependent slope of the linear potential. With a quadratic potential, the peak height and width of the rogue wave can be arbitrarily manipulated to result, for a special case, in a very intense pulse.     

Rogue wave observation in a water wave tank

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schr?dinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.     

Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa–Satsuma case

We present the lowest order rogue wave solution of the Sasa–Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of the Peregrine solution appears when the extension parameter of the SSE is reduced to zero.     

Nonlinear fast growth of water waves under wind forcing

In the wind-driven wave regime, the Miles mechanism gives an estimate of the growth rate of the waves under the effect of wind. We consider the case where this growth rate, normalised with respect to the frequency of the carrier wave, is of the order of the wave steepness. Using the method of multiple scales, we calculate the terms which appear in the nonlinear Schrödinger (NLS) equation in this regime of fast-growing waves. We define a coordinate transformation which maps the forced NLS equation into the standard NLS with constant coefficients, that has a number of known analytical soliton solutions. Among these solutions, the Peregrine and the Akhmediev solitons show an enhancement of both their lifetime and maximum amplitude which is in qualitative agreement with the results of tank experiments and numerical simulations of dispersive focusing under the action of wind.     

Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

The Peregrine breather of order eleven(P_(11) breather) solution to the focusing one-dimensional nonlinear Schrdinger equation(NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P_(11) breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the(x; t) plane, in function of the different parameters.     

Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

A new exactly solvable ($1+1$)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.     

Observation of rogue wave triplets in water waves

Doubly-localised breather solutions of the nonlinear Schrödinger equation (NLS) are considered to be appropriate models to describe rogue waves in water waves as well as in other nonlinear dispersive media such as fibre optics. Within the hierarchy of this type of formations, the Peregrine breather (PB) is the lowest-order rational solution. Higher-order solutions of this kind may be understood as a nonlinear superposition of fundamental Peregrine solutions. These superpositions are nontrivial and admit only a fixed well prescribed number of elementary breathers in each higher-order solution. Here, we report first observation of second-order solution which in reality is a triplet of rogue waves.     

Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations

Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation.In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions contain polynomials of the fourth order rather than the second order. Moreover, dark-brightrogue wave solutions of the coupled Hirota equations are given, and interactions between Peregrine solitons and dark-bright solitons are analyzed. The results further reveal the dynamical properties of rogue waves for the coupled Hirota equations.     

Changes in hydrogen isotope ratios in sequential plumage stages: an implication for the creation of isotope-base maps for tracking migratory birds

Accurate reference maps are important in the use of stable-isotopes to track the movements of migratory birds. Reference maps created by the analysis of samples collected from young at the nest site are more accurate than simply referring to naturally occurring patterns of hydrogen isotope ratios created by precipitation cycles. Ratios of hydrogen isotopes in the nutrients incorporated early in the development of young birds can be derived from endogenous, maternal sources. Base-maps should be created with the analysis of tissue samples from hatchlings after local the isotopic signature of exogenous nutrients is dominant. Migratory species such as Peregrine Falcons are known to use endogenous sources in the creation of their eggs, therefore knowledge of what plumage stage best represents the local hydrogen ratios would assist in the planning of nest visits. We conducted diet manipulation experiments involving Japanese Quail and Peregrine Falcons to determine the plumage stage when hydrogen isotope ratios were indicative of a switch in their food source. The natal down of both the quail and falcons reflected the diet of breeding adult females. The hydrogen isotope ratios of a new food source were dominant in the juvenile down of the young falcons, although a further shift was detected in the final juvenile plumage. The juvenile plumage is grown during weeks 3-4 after hatch on Peregrine Falcons. Nest visits for the purpose of collecting feathers for isotope-base-map creation should be made around 4 weeks after the presumed hatch of the young falcons.     

On solitary-wave interaction

We study analytically the interaction of the solitary waves of the regularized long-wave equation proposed by Peregrine and Benjamin et al. It is shown in the long-wave limit that the solitary waves interact inelastically, and that a new solitary wave as well as a radiation tail are generated as a result of the interaction. The result agrees with the numerical observation made by Bona et al. The analysis presented here can also be applied to the general weakly dispersive nonlinear wave systems, and it shows that the interaction property holds commonly for the nonintegrable systems.     

Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities

In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.     

Rogue wave triplets in an ion-beam dusty plasma with superthermal electrons and negative ions

A new dust ion-acoustic wave structure called ‘Rogue wave triplets’ is investigated in an unmagnetized plasma consisting of stationary negatively charged dust grains, charged positive and negative ions, and electrons obeying kappa distribution, which is penetrated by an ion beam. The reductive perturbation theory is used to derive the nonlinear Schrödinger equation governing the dynamics as well as the modulation of wave packets. The rogue wave triplets which are composed of three separate Peregrine breathers can be generated in the modulation instability region. It has been suggested that a laboratory experiment be performed to test the theory presented here.     

Al-0.5%Cu合金中表现反常振幅效应的低频位错内耗

用低频扭摆的方法,系统地研究了能够较有把握地观测到在Al-0.5％Cu合金中所出现的反常位错内耗的实验程序。结果指出,把试样在拉力试验机上预先拉伸到某一适当的形变量后,立即测量它在某一适当温度下时效的过程中的内耗,可以在内耗-时效时间曲线上观察到一个表现反常振幅效应(即内耗-振幅曲线上出现一个峯值)的时效内耗峯。用经过充分时效而内耗已经达到稳定值的试样,逐渐增加振幅,测量内耗,也可以观察到一个应变振幅内耗峯(当内耗表示为应变振幅的函数时)。此外,用一定的应变振幅在较高温度下,测量经过充分时效的试样的内耗时,也可以观察到一个表现反常振幅效应的温度内耗峯(当内耗表示为温度的函数时)。这些实验结果肯定地指出,在一定测量温度下的振幅内耗峯和表现反常振幅效应的温度内耗峯是存在的。为了找出以前在Al-0.5％Cu中所观察到的反常内耗现象重复性不好的原因,系统地研究了测量内耗所用的应变振幅对于出现振幅内耗峯的影响以及预形变量对于出现时效内耗峯和温度内耗峯的影响。对于出现反常内耗现象的实验条件进行了分析。所观察到的关于反常内耗现象的实验结果,都可用位错拖着溶质原子气团运动的模型来作定性的解释。具体的模型和理论分析将另行报导。     

New exact solutions of some nonlinear evolution equations of pseudoparabolic type

This paper aims to conduct an analytical study into some nonlinear models of pseudoparabolic type, including the Oskolkov, Oskolkov–Benjamin–Bona–Mahony–Burgers, and Benjamin–Bona–Mahony–Peregrine–Burgers equations. A number of new exact solutions for these pseudoparabolic type equations have been derived based on the modified Kudryashov method that its calculations are performed in a symbolic computation system known as Maple.     

Amplitude measurement of weak sinusoidal water surface acoustic wave using laser interferometer

To determine the amplitude of weak sinusoidal water surface acoustic wave(WSAW), a method based on the spectrum analysis of the phase-modulated interference signal is developed. Calculated from the amplitude spectrum of the detection signal, a characteristic ratio indicates that the phase-modulation depth of a WSAW is suggested by determining the amplitude of a WSAW according to their functional relationship. Experimental investigations for a 4 k Hz WSAW evaluate the measurement's precision with an amplitude measurement standard deviation of 0.12 nm. The measurement accuracy also is demonstrated by the experimental investigations.The theory of this method is briefly described, and the experimental setup is presented.     

Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analyzed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated.Linearized resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian non-linear stiffness is clearly demonstrated. The resonance peak is confined to a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. The forced response spectrum exhibits several harmonics because of a non-linear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results.For higher input amplitudes, the system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibro-impacting contact and leads to a wide frequency range softening resonance. The spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency vs. input amplitude allows the identification of the non-linear damping law during intermittent contact. Simulations of the vibro-impacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results.