A Simple Approach to Derive a Novel N-Soliton Solution for a （3＋1）-Dimensional Nonlinear Evolution Equation

Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a （3＋1）-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica.     

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

An analysis of the chaos suppression of a nonlinear elastic beam(NLEB)is presented.In terms of modal transformation the equation of NLEB is reduced to the Duffing equation.It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions.By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric pertubation to the same as the periodic one,the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.     

Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam

The propagation characteristics of nonlinear ion–acoustic(IA) solitary waves(SWs) are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries(KdV) equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons.     

Walk-off reduction,using an external optical plate and Bessel–Gaussian interaction

To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type ⅡKTiOPO_4 and type I β-BaB_2O_4 optical crystals,and the Gaussian output beam of a Q-switched Nd:YAG laser,a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness.By rotating the plate up to 35°along the beam direction,we reduced the walk-off angle up to ~ 13%.The same phenomenon is predicted by the model,confirming the performance of the model.It is found that,due to the walk-off effect,the intensity profile of the thirdharmonic generation beam is slightly degraded.To compensate for the observed phenomena and further reduce the walkoff,we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form.As a result,the walk-off is decreased to~ 48.81 mrad,providing ~ 30%relative reduction.By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction,the walk-off angle is further reduced to 38.9 mrad.Moreover,it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.     

Self-deflection of a bright soliton in a separate bright－dark spatial soliton pair based on a higher-order space charge field

The self-deflection of a bright solitary beam can be controlled by a dark solitary beam via a parametric coupling effect between the bright and dark solitary beams in a separate bright－dark spatial soliton pair supported by an unbiased series photorefractive crystal circuit. The spatial shift of the bright solitary beam centre as a function of the input intensity of the dark solitary beam (\hatρ) is investigated by taking into account the higher-order space charge field in the dynamics of the bright solitary beam via both numerical and perturbation methods under steady-state conditions. The deflection amount (Δs_0), defined as the value of the spatial shift at the output surface of the crystal, is a monotonic and nonlinear function of \hatρ. When \hatρ is weak or strong enough, Δs_0 is, in fact, unchanged with \hatρ, whereas Δs_0 increases or decreases monotonically with \hatρ in a middle range of \hatρ. The corresponding variation range (δs) depends strongly on the value of the input intensity of the bright solitary beam (r). There are some peak and valley values in the curve of δs versus r under some conditions. When \hatρ increases, the bright solitary beam can scan toward both the direction same as and opposite to the crystal's c-axis. Whether the direction is the same as or opposite to the c-axis depends on the parameter values and configuration of the crystal circuit, as well as the value of r. Some potential applications are discussed.     

A Simple Model for Nonlinear Confocal Ultrasonic Beams

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov （KZK） equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.     

Soliton guidance and nonlinear coupling for polarized vector spiraling elliptic Hermite–Gaussian beams in nonlocal nonlinear media

We investigate the incoherent beams with two orthogonal polarizations in nonlocal nonlinear media, one of which is a fundamental Gaussian beam and the other is spiraling elliptic Hermite–Gaussian beam carrying the orbital angular momentum(OAM).Using the variational approach, we obtain the critical power and the critical OAM required for the vector spiraling elliptic Hermite–Gaussian solitons.In the strong nonlocality region, two components of the vector beam contribute to the nonlinear refractive index in a linear manner by the sum of their respective power.The nonlinear refractive index exhibits a circularly symmetrical profile in despite of the elliptic shapes for spiraling Hermite–Gaussian beams.We find that in the strong nonlocality region, the critical power and the rotational velocity are the same regardless of the relative ratio of the constituent powers.The nonlinear refractive index loses its circular symmetry in weak nonlocality region, and the nonlinear coupling effect is observed.Due to the radiation of the OAM, the damping of the rotation is predicted, and can be suppressed by decreasing the proportion of the spiraling elliptic component of the vector beam.     

Asymptotic solution for a class of sea-air oscillator model for El Nin^～o-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents axe an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr~dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg-de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr?dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg－de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

All-optical switchings of 3-hydroxyflavone in different solvents

3-hydroxyflavone （3-HF） is an organic molecule with an excited-stated intramolecular proton transfer （ESIPT） effect. All-optical switchings and beam deflections of 3-HF in three kinds of solvents （cyclohexane, ethanol and dimethyl sulfoxide） have been investigated by using the third-harmonic generation （355 nm） of a mode-locked Nd：YAG laser as a pump beam and a continuous-wave （cw） He-Ne laser （632.8 nm） as a probe beam. The nonlinear refractive indices of 3-HF in the three different solvents are determined by using the Z-scan technique under an ultraviolet （UV） pump beam at a wavelength of 355 nm. It has been found that the optical switching and beam deflection effects result from the change in refractive index of 3-HF under the irradiation of the pump beam. On the basis of the analyses of absorption spectra and fluorescence spectra, we conclude that the change in refractive index of 3-HF is due to not the thermal effect but the ESIPT effect of 3-HF under the pump beam. As the ESIPT is exceedingly fast, 3-HF might be an excellent candidate for high-speed optical switching.     

Transformation of general astigmatic Gaussian beams in a four-dimensional phase space

A phase space model of two-dimensional (2D) Gaussian beam propagation is generalized for three-dimensional (3D) general astigmatic Gaussian beam passing through first-order optical system. The general astigmatic Gaussian beam is represented by a four-dimensional (4D) phase super-ellipsoid that defined by an associated 4×4 real matrix, then the transformation formula of the phase super-ellipsoid of the beam through first-order optical system is derived. In particular, in the phase space framework, the beam propagation factor M2 value is proved to be a ratio of phase area of real beam to ideal beam, and a novel approach for a qualitative examination of the properties of fractional Fourier transform (FRT) for the beam is also provided.     

Stimulated Raman Scattering in Bi-temperature Vlasov Plasma

We obtain the nonlinear coupling equations for describing stimulating Raman scattering (SRS) of ultra-intense laser beam starting from the relativistic Vlasov-Maxwell equations. It is found that the relativistic electrons play an important role in the inhibition of the SRS instability and the growth rate of backward SRS strongly decreases with the increasing number of relativistic electrons.     

Propagation characteristics of a high-power beam in weakly relativistic-ponderomotive thermal quantum plasma

The present work explores the propagation characteristics of high-power beams in weakly relativistic-ponderomotive thermal quantum plasma. A q-Gaussian laser beam is taken in the present investigation. The quasi-optics equation obtained in the present study is solved through a well-established Wentzel–Kramers–Brillouin approximation and paraxial theory approach for obtaining the second-order differential equation describing the behavior of beam width of the laser beam. Further, a numerical simul...     

Stability of Bright Solitons in Bose-Einstein Condensates

We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Oross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.     

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.     

Large negative Goos-H(a|¨)nchen shift from a wedge-shaped thin film

The analytical expression for the complex amplitude of light reflected from a wedge-shaped thin film is derived. For plane wave incidence, a simple ray tracing approach is used to calculate Goos-H(a|¨)nchen (GH) shifts; and for non-plane wave incidence, for example, a Gaussian beam, the angular spectrum approach of plane wave is used in simulation. The two approaches predict that a wedge-shaped thin film can produce large negative longitudinal GH shifts. Although the reflectivity is small near the condition...     

Stochastic perturbation in quasi—ideal dispersion—managed soliton system

The model of stochastic perturbation is built up systematically in quasi-ideal dispersion-managed soliton system,its influence on soliton propagation is investigated by both the variational approach and the numerical simulation,and it is found that the stochastic perturbation leads to disintegration of soliton and enhances the interaction between solitons.The nonlinear gain and filter are introduced to suppress effectively the influence on both soliton propagation and interaction.     

Bose—Einstein Condensation in a Spherical Symmetric Harmonic Trap

Using a perturbation theory approach,we derive an approximate analytical solution of the Gross-Pitaevskii equation in a spherical symmetric harmonic trap.This solution is consistent with that obtained numerically.     

Analytical model of an acoustic diode comprising a superlattice and a nonlinear medium

We give an analytical analysis to the acoustic propagation in an acoustic diode (AD) model formed by coupling a superlattice (SL) with a nonlinear medium. Analytical solutions of the acoustic transmission are obtained by studying the propagations in the SL and the nonlinear medium separately with the conventional transfer-matrix method and a perturbation technique. Compared with the previous numerical method, the proposed approach contributes a better physical insight into the intrinsic mechanism of acoustic rectification and helps us to predict the performance of an AD within the effective rectifying bands in a simple way. This is potentially significant for the practical design and fabrication of AD devices.