Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger （CCQNLS） equations through the generalized Darboux transformation （DT）. A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed：（i） the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; （ii） hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; （iii） hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system.

Nonisospectral effects on generating localized waves

In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media.The nonisospectral Korteweg–de Vries,modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the idea.Their solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.

Localized Optical Waves in Defocusing Regime of Negative-Index Materials

We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.

One-Dimensional Localization of Elastic Waves in Rib-Stiffened Plates

The 1 dimensional localization of elastic waves in disordered periodic multi span rib stiffened plates is investigated. The transfer matrix method is employed to obtain the transfer matrix of the system, and the method for calculating the Lyapunov exponents in continuous dynamic systems presented by Wolf is used to determine the localization factor. As examples, the numerical results of the localization factors are given for a disordered rib stiffened plate. The effects of the degree of disorder of span...

Localized Effect of Light Diffraction by Capillary Wave

The localized effect of light diffracted by a capillary wave is discovered by changing the wave amplitude. The localized range is related to the wave number and the amplitude. The dependence of the half maximum localized angle on the wave number and amplitude is analytically derived. Meanwhile, the analytic angular distribution of the diffraction light in the localized range is obtained. Experiments are carried out to achieve diffraction patterns to confirm the localized effect and to measure the angular distribution of the diffraction light intensity as well as to determine the localized range scales corresponding to different wave amplitudes. Theoretical curves of the light intensity angular distribution and localized interval widths related to surface acoustic wave amplitudes are compared with the experimental data. The experimental results agree well with the theoretical prediction.

Shear wave splitting analysis of local earthquakes from dense arrays in Shimian,Sichuan

The Shimian area of Sichuan sits at the junction of the Bayan Har block.Sichuan-Yunnan rhombic block,and Yangtze block,where several faults intersect.This region features intense tectonic activity and frequent earthquakes.In this study,we used local seismic waveform data recorded using dense arrays deployed in the Shimian area to obtain the shear wave splitting parameters at 55 seismic stations and thereby determine the crustal anisotropic characteristics of the region.We then analyzed the crustal stress pattern and tectonic setting and explored their relationship in the study area.Although some stations returned a polarization direction of NNW-SSE.a dominant polarization direction of NW-SE was obtained for the fast shear wave at most seismic stations in the study area.The polarization directions of the fast shear wave were highly consistent throughout the study-area.This orientation was in accordance with the direction of the regional principal compressive stress and parallel to the trend of the Xianshuihe and Daliangshan faults.The distribution of crustal anisotropy in this area was affected by the regional tectonic stress field and the fault structures.The mean delay time between fast and slow shear waves was 3.83 ms/km.slightly greater than the values obtained in other regions of Sichuan.This indicates that the crustal media in our study area had a high anisotropic strength and also reveals the influence of tectonic complexity resulting from the intersection of multiple faults on the strength of seismic anisotropy.

Slip boundary effect on the critical Reynolds number of subcritical transition in channel flow

In this letter,the effect of slip boundary on the origin of subcritical transition in two-dimensional chan-nel flows is studied numerically and theoretically.It is shown that both the positive and the negative slip lengths will increase the critical Reynolds number of localized wave packet and hence postpone the transition.By applying a variable transformation and expanding the variables about a small slip length,it is illustrated that the slip boundary effect only exists in the second and higher order modulations of the no-slip solution,and hence explains the power law found in simulations,i.e.the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.

Mesh Smoothing Method Based on Local Wave Analysis

As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.

FLEXURAL WAVE PROPAGATION IN NARROW MINDLIN'S PLATE

Appling Mindlin＇s theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories, the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.

Fault Diagnosis of a Rotor Based on a Lifting Wavelet and Local Wave

Aiming at the mode mixture in local wave decomposition（LWD） caused by a noise signal, the original data is preprocessed using the lifting wavelet transformation to suppress abnormal interference of noise and improve the quality of decomposition. It is employed to analyze the vibration signal of rotor rub-impact for extracting the weak impulsive feature. The signal is decomposed into intrinsic mode functions by LWD, then the high-frequency components are analyzed by Hilbert envelop demodulation. The period of the impulse response can be achieved, and the modulate fault feature of the vibration signal of a rotor system with rub-impact fault can be extracted exactly. Analysis results show that the proposed method is accurate and efficient, and is expected to be applied in engineering practice effectively.

Principle and Experimental Verification of Flexible Caudal Fin Based on Active Torsion Propulsion Mode

The active torsion propulsion mode of a caudal fin,composed of macro fiber composites(MFC)and carbon fiber orthotropic composite material is proposed.The caudal fin is excited by the piezoelectric structure to vibrate flexibly.The work principle is firstly analyzed by finite element method(FEM)and experiments.Then the caudal fin is optimized to increase the torque and improve the streamline,and the added mass effect from the water is discussed in terms of the frequency of the structure.The torsion resonance frequency is around 103 Hz in the air and decreased by 75%to 25 Hz in the water.Finally,the mean thrust is discussed and measured to be 11 mN at900V(Peak to peak)driving voltage.A flexible micro robot is developed and tested.The locomotion velocity and flow velocity is 320mm/s and 268mm/s,respectively.The results of the simulation and experiments indicate that the locomotion of the biomimetic aquatic robot has fast movement characteristics.

Application of Wavelet Packet De-noising in Time-Frequency Analysis of the Local Wave Method

The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.

Application of Local Wave Time-Frequency Spectrum and Neural Networks to Fault Classification in Rotating Machine

A new method of fault analysis and detection by signal classification inrotating machines is presented. The Local Wave time-frequency spectrum which is a new method forprocessing a non-stationary signal is used to produce the representation of the signal. This methodallows the decomposition of one-dimensional signals into intrinsic mode functions (IMFs) usingempirical mode decomposition and the calculation of a meaningful multi-component instantaneousfrequency. Applied to fault signals , it provides new time-frequency attributes. Then the momentsand margins of the time-frequency spectrum are calculated as the feature vectors. The probabilisticneural network is used to classify different fault modes. The accuracy and robustness of theproposed methods is investigated on signals obtained during the different fault modes (early rub,loose, misalignment of the rotor).

Local Pulse Wave Velocity Estimation in the Carotids Using Dynamic MR Sequences

The current study presents a new protocol for local pulse wave velocity (PWV) measurement using dynamic MR sequences, which have a high temporal resolution (TR < 6 ms). MR images were obtained at two positions along the common carotid artery, separated by a distance of 5 cm. In each phase of a MR series, carotid region was automatically extracted and then its area distension waveform could be obtained. Sixteen volunteers with no symptoms of cardiovascular diseases were studied. For local PWV estimation, three delay estimation principles were tested and produced the following values: intersecting tangents method (M1): 4.72 ± 1.40 m/s, second derivative method (M2): 4.94 ± 1.68 m/s and cross-correlation method (M3): 5.03 ± 1.17 m/s. The cross-correlation method showed a relative high reliability as its least standard deviation.

A PERIODICALLY LOCALIZED TRAVELING WAVE STATE OF BINARY FLUID CONVECTION WITH HORIZONTAL FLOWS

In this paper, the convection structure in a rectangular channel with a horizontal flow was studied for the aspect ratio ГA=12 and the separation ratio ψ=-0.11. Our simulations were preformed by solving the hydrodynamic equations using the SIMPLE method. In the system of binary fluid convection with a horizontal flow, a Periodically Localized Traveling Wave （PLTW） state was found. It has similar behavior to classical Rayleigh-Benard convection in a binary fluid mixture, but the region and wave number of convection change periodically with time. The instability of PLTW depends on the Rayleigh number r and the intensity of horizontal flows Re for given ψ. Thus, the PLTW convection results from the competition between the horizontal flow and the counter-propagating wave near the onset of convection.

Novel localized wave solutions of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Based on a special transformation that we introduce,the N-soliton solution of the(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed.By applying the long wave limit and restricting certain conjugation conditions to the related solitons,some novel localized wave solutions are obtained,which contain higher-order breathers and lumps as well as their interactions.In particular,by choosing appropriate parameters involved in the N-solitons,two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution.Five solutions including two breathers,two lumps,and interaction solutions between one breather and two bell-shaped solitons,one breather and one lump,or one lump and two bell-shaped solitons are constructed from the4-soliton solution.Five interaction solutions mixed by one breather/lump and three bell-shaped solitons,two breathers/lumps and a bell-shaped soliton,as well as mixing with one lump,one breather and a bell-shaped soliton are constructed from the 5-soliton solution.To study the behaviors that the obtained interaction solutions may have,we present some illustrative numerical simulations,which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties.The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations.The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.

DYNAMICS OF LOCALIZED TRAVELING WAVE CONVECTION IN BINARY FLUID MIXTURE

The dynamical behavior of a localized traveling wave (LTW) in a binary fluid layer heated from below confined in a rectangular cell with the intermediate aspect ratio Γ=12 and the separation ratio ψ=-0. 11 is studied by using the two-dimensional numerical simulation of the full hydrodynamic equations. We find that a counterpropa-gating wave (CPW) occurs at the onset of convection and is modulated in space-time. The modulated traveling wave (MTW) plays an important role in the transition to the LTW state, and the LTW state depends on the fluid parameters and exists in a narrow interval of the reduced Rayleigh number. The transition from LTW to an extended traveling wave (ETW) or stationary overturning convection (SOC) state occurs when r exceeds a certain critical value. Our results agree with those observed in experiments.

THE SPATIO-TEMPORAL STRUCTURE OF BINARY FLUID CONVECTION WITH HORIZONTAL FLOW

The convection structure in a rectangular channel with a horizontal flow forΓ = 12 was studied. The simulations were preformed by solving the hydrodynamic equations using theSIMPLE method. The convective behavior in an absolutely and convectively unstable regime wasstudied. The results show that the two types of convection patterns in this system appear dependingon the convection intensity and horizontal flow. A periodically localized traveling wave state wasfound in this system.

A comparative study of wave localization in locally resonant Thue–Morse, Rudin–Shapiro and Period-Doubling aperiodic structures

The localization characteristics of the in-plane elastic waves in locally resonant aperiodic phononic crystals are examined in this study. In particular, the phononic crystals generated according to the Thue-Morse, Rudin-Shapiro and Period-Doubling sequences are theoretically investigated by using the extended transfer matrix method. For comparison, the binary and ternary locally resonant systems are considered, and their band structures are characterized by using the localization factors. Moreover, the influences of structural arrangement, material combination, incidence angle, number of components, length ratio, and random disorder on the band structures are also discussed. Some novel and interesting phenomena are observed and discussed.