Orbital Stability of Solitary Waves for Generalized Zakharov System

In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov

Dolphin Vocal Sound Generation via Deep WaveGAN

The marine biological sonar system evolved in the struggle of nature is far superior to the current artificial sonar. Therefore, the development of bionic underwater concealed detection is of great strategic significance to the military and economy. In this paper, a generative adversarial network(GAN) is trained based on the dolphin vocal sound dataset we constructed, which can achieve unsupervised generation of dolphin vocal sounds with global consistency. Through the analysis of the generated audio samples and the real audio samples in the time domain and the frequency domain, it can be proven that the generated audio samples are close to the real audio samples,which meets the requirements of bionic underwater concealed detection.

Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation

We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.

Global Well-posedness of the Generalized Long-short Wave Equations

In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.

Generalized Rayleigh Wave Dispersion in a Covered Half-space Made of Viscoelastic Materials

Dispersion of the generalized Rayleigh waves propagating in a covered halfspace made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity.The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration.Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time,long-term values and the mechanical behaviour of the viscoelastic material around the initial state of the deformation.Numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov.As the result of this discussion,in particular,how the rheological parameters influence the dispersion of the generalized Rayleigh waves propagating in the covered half-space under consideration is established.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

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.

Travelling Wave in the Generalized Kuramoto Model with Inertia

We study the dynamics of the generalized Kuramoto model with inertia, in which oscillators with positive cou- pling strength are conformists and oscillators with negative coupling strength are contrarians. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already displayed travelling wave states and π state in previous be characterized by the phase distributions of oscillators. travelling wave state of the model in the parameter space literature. The modulated travelling wave state may Finally, the modulated travelling wave state and the are presented.

Generalized Wave Operators in Von Neumann Algebras

Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).

Construction of Recursion Formulas for Lax Pairs of (2+1)-Dimensional Equation: Modified Generalized Dispersive Long Wave Equation

In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.

A meshless method for the nonlinear generalized regularized long wave equation

This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the.scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method.

Plasma Simulation of Dielectric-lined Multiwave Cerenkov Generators Producing High Power Millimeter Waves

This paper presents the concept of a Dielectric-lined Multiwave Cerenkov Generator producing high power millimeter waves, which has been investigated with a two and onehalf dimensional electromagnetic relativistic Particle-in-Cell (PIC) plasma simulation code. Themodified device can operate in a lower diode-voltage regime with much higher radiation efficiencyand slight downshift of operation frequency. There exist the optima for the permittivity of thedielectric liner and for the magnitude of the guiding magnetic field. The required intensity of theguiding field is reduced by the introduction of the liner. The enhanced propagation of the electronbeam is studied in the presence of the liner.

Generalized collar waves in acoustic logging while drilling

Tool waves, also named collar waves, propagating along the drill collars in acoustic logging while drilling （ALWD）, strongly interfere with the needed P- and S-waves of a penetrated formation, which is a key issue in picking up formation P- and S-wave velocities. Previous studies on physical insulation for the collar waves designed on the collar between the source and the receiver sections did not bring to a satisfactory solution. In this paper, we investigate the propagation features of collar waves in different models. It is confirmed that there exists an indirect collar wave in the synthetic full waves due to the coupling between the drill collar and the borehole, even there is a perfect isolator between the source and the receiver. The direct collar waves propagating all along the tool and the indirect ones produced by echoes from the borehole wall are summarized as the generalized collar waves. Further analyses show that the indirect collar waves could be relatively strong in the full wave data. This is why the collar waves cannot be eliminated with satisfactory effect in many cases by designing the physical isolators carved on the tool.

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile.Considering the tooth influence on the position of equivalent neutral layer,a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper.Firstly,a mechanic model of a ring of uniform thickness in contact with a rigid cam is established.The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium rela-tionship,respectively.Meanwhile,the wrapping angle is solved according to the boundary conditions.The assembly forces are derived to investigate the circumferential elongation and strain.Then,considering the tooth effects on the neutral layer of flexspline,the tooth is positioned on the equivalent neutral layer,which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer.The equivalent neutral layer is positioned by the empirical formula of the offset ratio,which is summarized by the orthogonal simulation on finite element models of racks.Finally,finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method.The results show that,compared with the geometric method,the tooth positioning deviation calculated by the piecewise method can be reduced by about 70%with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

In this paper,the generalized Boussinesq wave equation u tt-uxx+a(um) xx+buxxxx=0 is investigated by using the bifurcation theory and the method of phase portraits analysis.Under the different parameter conditions,the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.

Oscillatory Flow in Thermoacoustic Sound Wave Generator

Oscillatory flow in a thermoacoustic sound wave generator is described. The thermoacoustic sound wave generator plays an important role in thermoacoustic equipment. The heat exchange between the working fluid and the stack, the acceleration and deceleration of the working fluid and viscous friction loss both in the stack and in the resonance tube influence the performance of the thermoacoustic sound wave generator. Particularly, oscillatory flow significantly influences the heat exchange mechanism between the working fluid and the stack. Temporal changes in pressure and velocity are sinusoidal inside the resonance tube. Flow forms an oscillatory jet just behind the tube outlet, and becomes intermittent far downstream outside the resonance tube. The open-end corrections of 0.63R, that is, the region where oscillatory flow characteristics are maintained downstream in spite of being outside the tube outlet, are confirmed by velocity measurements and flow visualization. Also, they are almost equal to acoustical theoretical results.

GLOBAL SOLUTION AND ITS LONG TIME BEHAVIOR FOR THE GENERALIZED LONG-SHORT WAVE EQUATIONS

The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.

Abundant closed form wave solutions to some nonlinear evolution equations in mathematical physics

The propagation of waves in dispersive media,liquid flow containing gas bubbles,fluid flow in elastic tubes,oceans and gravity waves in a smaller domain,spatio-temporal rescaling of the nonlinear wave motion are delineated by the compound Korteweg-de Vries(KdV)-Burgers equation,the(2+1)-dimensional Maccari system and the generalized shallow water wave equation.In this work,we effectively derive abundant closed form wave solutions of these equations by using the double(G′/G,1/G)-expansion method.The obtained solutions include singular kink shaped soliton solutions,periodic solution,singular periodic solution,single soliton and other solutions as well.We show that the double(G′/G,1/G)-expansion method is an efficient and powerful method to examine nonlinear evolution equations(NLEEs)in mathematical physics and scientific application.