Nonautonomous Solitons in the(3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrdinger equation in the(3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium.The gain parameter has no effects on the motion of the soliton's phase or their velocities,and it affects just the evolution of their peaks.As two examples,we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system.Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly,but also broadens their width.

The similarity of interactions between (3+1)D spatiotemporal optical solitons in both the dispersive medium with cubic-quintic nonlinearity and the saturable medium

By making use of the split-step Fourier method, this paper numerically simulates dynamical behaviors, including repulsion, fusion, scattering and spiraling of colliding （3＋1）D spatiotemporal solitons in both the dispersive medium with cubic-quintic and the saturable medium. Careful comparison of the colliding behaviors in these two media is presented. Although the origin of the nonlinearities is different in these two media, the obtained results show that the dynamical behaviors are very similar. This presents additional evidence to support the supposition of universality of interactions between solitons.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.

Generation of breathing solitons in the propagation and interactions of Airy–Gaussian beams in a cubic–quintic nonlinear medium

Using the split-step Fourier transform method, we numerically investigate the generation of breathing solitons in the propagation and interactions of Airy–Gaussian（AiG） beams in a cubic–quintic nonlinear medium in one transverse dimension. We show that the propagation of single AiG beams can generate stable breathing solitons that do not accelerate within a certain initial power range. The propagation direction of these breathing solitons can be controlled by introducing a launch angle to the incident AiG beams. When two AiG beams accelerated in opposite directions interact with each other,different breathing solitons and soliton pairs are observed by adjusting the phase shift, the beam interval, the amplitudes,and the light field distribution of the initial AiG beams.

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores＇ nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.

Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.

GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π~2+ Le C, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.

Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM

The nonlocal nonlinear vibration analysis of embedded laminated micro- plates resting on an elastic matrix as an orthotropic Pasternak medium is investigated. The small size effects of micro/nano-plate are considered based on the Eringen nonlocal theory. Based on the orthotropic Mindlin plate theory along with the von Kármán geo- metric nonlinearity and Hamilton＇s principle, the governing equations are derived. The differential quadrature method （DQM） is applied for obtaining the nonlinear frequency of system. The effects of different parameters such as nonlocal parameters, elastic me- dia, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate. Results show that considering elastic medium increases the nonlinear frequency of system. F^lrthermore, the effect of boundary conditions becomes lower at higher nonlocal parameters.

Bistability in a Hybrid Optomechanical System under the Effect of a Nonlinear Medium

We investigate a hybrid optomechanical system consisting of two coupled cavities, one of them is composed of two-end fixed mirrors （called the traditional cavity）, and the other has a one-end oscillating mirror （named as the optomechanical cavity）. A Kerr medium is inside the traditional cavity to enhance the nonlinearity due to the fact that it can cause observing of bistable behavior in intracavity intensity for the optomechanical cavity. The Hamiltonian of the system is written in a rotating frame and its dynamics is described by quantum Langevin equations of motion. Our proposed system exhibits unconventional plots for the mean photon number of the optomechanical cavity which are not observed in previous works. The present results show a deep effect of the Kerr medium on optical bistability of intracavity intensity for the optomechanical cavity. Also, coupling strength of the cavities can effectively change the stability of the system.

A Class of Cauchy Problems for Porous Medium Equations with Strongly Nonlinear Sources and Convections

In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.

A PERTURBATION BOUNDARY INTEGRAL EQUATION METHOD FOR ANALYSIS OF INTERACTION BETWEEN FOUNDATION AND NONLINEAR ROCK AND SOIL MEDIUM

A scheme is developed for analysing the interaction between afoundation and a nonlin- ear rock and soil medium, in which thefoundation is considered as a linear elastic body and a typicalboundary integral equation method (BIEM) is employed. On the basis oftaking the nonlinear proper- ties of the medium into account, aperturbation BIEM is developed. The fundamental equations for thenonlinear coupling analysis are formulated, and typical problems aresolved and discussed by the pre- sent method.

含分布式电源及储能系统的配电网最优配置研究

针对大量分布式电源与储能系统接入电网,为有效对配电网系统进行配置、实现其优化经济运行,提出了配电系统中电池储能系统和分布式发电机的最优配置方法,建立混合整数非线性规划模型并采用规划-运行分解方法进行求解。采用一种定义邻域结构的模拟退火算法,提出分解方法来求解储能系统运行状态问题,以较低计算量来保证近全局最优解。最后,在一个包含230个节点的中低压配电系统上测试了所提出的规划-运行分解方法,利用规划-运行方法进行配置。结果表明,同时接入储能系统和分布式发电并进行合适的配置,其收益较高,虽成本也有所增加,但具有长期收益。同时验证了配置方法的有效性和可行性。

泥石浆型复杂破碎岩体非线性渗流数学模型与实验研究

断层、陷落柱是影响承压水上煤层开采的主要隐患之一,由于其具有碎石块和泥质充填物(泥石浆)构成的复杂结构,其渗透性的确定通常以定性分析为主,缺少量化模型。为了研究泥石浆型复杂破碎岩体渗透性的量化计算方法,开展了渗流实验研究破碎岩体非线性渗流规律,并基于多孔介质分形理论、非线性渗流理论,建立了考虑黏土成分及泥化充填作用的破碎岩体非线性渗流数学模型,最后与实验结果对比验证数学模型的准确性。结果表明:①陷落柱破碎带样品的粒度分布具有一定的分形规律,含有黏土颗粒的破碎带岩体遇水泥化后,分形维数增大,黏土充填封堵了大颗粒岩石碎块内部的大孔隙,降低了破碎岩体的渗透性;②随着破碎带岩体渗透率的降低,非线性开始发生时的临界压力梯度也增大,表明非线性临界压力梯度可以用来量化破碎岩体的阻隔水能力;③非线性开始发生时的临界压力梯度的实验结果与数学模型计算结果吻合,验证了模型的准确性。建立的破碎岩体非线性渗流数学模型首次尝试考虑了黏土成分及泥化充填作用对渗透性的影响,为泥石浆型复杂破碎岩体渗透性的定量计算及水体下、承压水上等特殊开采条件下地质构造的阻隔水性能研究提供了一种新的研究思路。

基于历史天气的区域电网负荷预测

随着社会经济的迅速发展,人们对电能的需要日益增加,但是在电网运行中,常常会出现电力产能过剩或者不足的情况,为保证电力系统安全稳定、经济运行,就必须掌握各种区域电网负荷的变化规律和发展趋势。论文对重庆市区供电分公司供电区域电网中长期负荷进行预测,提出一种预测区域电网中长期负荷的方法,即一种基于前12个月历史天气条件和区域电网负荷关联关系的多元非线性拟合的特征参数因子曲线的中长期负荷预测方法,建立基于不同算法的多种预测模型,通过归一化处理,得到的区域电网中长期负荷预测的精度高,与实际区域电网负荷之间的误差小,对于区域电网中长期负荷预测分析具有重要参考利用价值。

充填体—边界介质组合体剪切力学特性与参数分析

充填体—边界介质组合体接触面的剪切力学特性与参数是研究充填采场应力分布与充填体揭露稳定性评价的基础数据。通过室内直剪试验与RFPA^(3D)数值模拟试验联合手段,对3种灰砂配比(1∶4、1∶8和1∶20)、4种接触面法向应力(50 k Pa、100 k Pa、150 k Pa和200 k Pa)的充填体—边界介质组合体(充填体—围岩、充填体—矿体、胶结充填体—非胶结充填体)的剪切力学特性与声发射特征、黏聚力和内摩擦角参数变化规律进行了分析。结果表明:随灰砂配比降低,充填体—围岩组合体峰值剪切强度减少,破坏模式由脆性变为延性,破坏形态由颗粒粘连、块状粘连到凸起体尖端被剪断。灰砂配比1∶4组合体发生破坏时剪切应力垂直下降,振铃计数率突然骤增,其他阶段振铃计数率相对较小。灰砂配比1∶8和1∶20组合体从裂隙压密到破坏阶段,声发射振铃计数率密集,剪切过程中有明显剪胀变形;充填体—边界介质组合体接触面的峰值剪切强度随法向应力、灰砂配比降低而减少。胶结充填体—围岩接触面峰值剪切强度略小于胶结充填体—矿体强度,胶结—非胶结充填体组合体峰值强度远小于胶结充填体—矿岩组合体,接近非胶结充填体自身强度;充填体—边界介质组合体接触面的黏聚力和内摩擦角随灰砂配比降低而减少。充填体—围岩与充填体—矿体黏聚力和内摩擦角接近,胶结—非胶结充填体组合体黏聚力和内摩擦角参数远小于胶结充填体—矿岩组合体。研究结果拓展了充填体—边界介质组合体剪切力学特性获取方法,为充填采场稳定性分析提供了基础数据。

冲击荷载下岩土介质非线性振动预测方法研究

水利工程作为国家重点保护的民生工程,可能会承受军事打击、恐怖袭击、爆破施工等潜在的冲击荷载,因冲击荷载作用的强非线性,现有振动预测方法均存在不足之处。基于理论分析,提出一种能够精确预测冲击荷载下非线性振动的方法,并建立冲击荷载下岩土介质振动预测模型,通过大量现场实验验证方法及模型的准确性和实用性,为水利工程的安全防护提供理论依据。

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method （EMM） is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd （Gaunaurd GC and UEberall H, J. Acoust, Soc, Am., 1978; 63： 1699-1711） is employed to verify the EMM under linear approximation by comparing the dynamic （i.e. frequency-dependent） effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail, The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave, Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system＇s resonance induced by the existence of bubbles.

A quasi-discrete Hankel transform for nonlinear beam propagation

We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.

Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear Schrodinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium

Twin-core optical fibers are applied in such fields as the optical sensing and optical communication,and propagation of the pulses,Gauss beams and laser beams in the non-Kerr media is reported.Studied in this paper are the coupled cubic-quintic nonlinear Schrodinger equations with variable coefficients,which describe the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical fiber or non-Kerr medium.Based on the integrable conditions,bilinear forms are derived,and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction.Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis.With different values of the delayed nonlinear response effect b(z),where z represents direction of the propagation,the linear-and parabolic-shaped one dark-dark soltions can be derived.Interactions between the parabolic-and periodic-shaped two dark-dark solitons are presented with b(z)as the linear and periodic functions,respectively.Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed.Interactions between the two dark-dark solitons of different types are displayed,and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z.We find that those interactions are elastic.