Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

WAVE1、MMP-2及MMP-9在卵巢癌组织中的表达及意义

目的探讨WASP家族富含脯氨酸同源蛋白1(WASP-family verprolin-homologous protein 1,WAVE1)及基质金属蛋白酶-2(matrix metalloproteinases-2,MMP-2)和基质金属蛋白酶-9(MMP-9)在卵巢癌的表达及临床意义。方法采用免疫组化SABC三步法检测47例卵巢癌、30例卵巢良性肿瘤和21例正常卵巢组织中WAVE1、MMP-2、MMP-9的表达,并对卵巢癌组织WAVE1与MMP-2、MMP-9的表达进行相关性分析。结果①WAVE1、MMP-2及MMP-9在卵巢癌中的表达均高于在正常卵巢组织及卵巢良性组织中的表达,差异有统计学意义(P<0.05);Spearman相关分析显示,WAVE1和MMP-2、MMP-9两两表达成正相关(r=0.773,r=0.664,P<0.05)。②WAVE1的表达与卵巢癌的临床分期、组织分化及Ca-125水平有关(P<0.05),与年龄、肿瘤的直径无关(P>0.05)。MMP-2、MMP-9表达与卵巢癌的临床分期有关(P<0.05),与年龄、组织分化、Ca-125水平及肿瘤直径无关(P>0.05)。结论 WAVE1和MMP-2、MMP-9在卵巢癌中呈现高表达,早期联合筛查WAVE1和MMP-2、MMP-9指标对卵巢癌病情演变和预后评估有着重要的临床意义。

Periodic oscillation and fine structure of wedge-induced oblique detonation waves

An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections：the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.

Measurements of non-equilibrium and equilibrium temperature behind a strong shock wave in simulated martian atmosphere

Non-equilibrium radiation measurements behind strong shock wave for simulated Martian atmosphere are presented in this paper. The shock wave is established in a hydrogen oxygen combustion driven shock tube. Time- resolved spectra of the Av = 0 sequence of the B^2∑^＋ → X^2∑^＋ electronic transition of CN have been observed through optical emission spectroscopy （OES）. A new method, which is based on fitting high resolution spectrum for rotational and vibrational temperatures measurement, is proposed to diag- nose temperature distribution behind the shock wave. It is estimated that the current scheme has the maximum deviation less than 8% （lσ） for vibrational temperature measurement through detailed analysis of the influence of the uncertainties of spectroscopic constants and spectral resolution. Radiation structure of the shock layer, including induction, relaxation and equilibrium process, and corresponding rotational and vibrational temperatures are obtained through time gating OES diagnostics with sub-microsecond temporal resolution. The present extensive results will strongly benefit the reaction rate estimation and computational fluid dynamics （CFD） code validation in high enthalpy Mars reentry chemistry.

3D v_P and v_S models of southeastern margin of the Tibetan plateau from joint inversion of body-wave arrival times and surface-wave dispersion data

A new 3D velocity model of the crust and upper mantle in the southeastern （SE） margin of the Tibetan plateau was obtained by joint inversion of body- and sur- face-wave data. For the body-wave data, we used 7190 events recorded by 102 stations in the SE margin of the Tibetan plateau. The surface-wave data consist of Rayleigh wave phase velocity dispersion curves obtained from ambient noise cross-correlation analysis recorded by a dense array in the SE margin of the Tibetan plateau. The joint inversion clearly improves the Vs model because it is constrained by both data types. The results show that at around 10 km depth there are two low-velocity anomalies embedded within three high-velocity bodies along the Longmenshan fault system. These high-velocity bodies correspond well with the Precambrian massifs, and the two located to the northeast of 2013 Ms 7.0 Lushan earthquake are associated with high fault slip areas during the 2008 Wenchuan earthquake. The aftershock gap between 2013 Lushan earthquake and 2008 Wenchuan earthquake is associated with low-velocity anomalies, which also acts as a barrier zone for ruptures of two earthquakes. Generally large earthquakes （M 〉 5） in the region occurring from 2008 to 2015 are located around the high-velocity zones, indicating that they may act as asperities for these large earthquakes. Joint inversion results also clearly show that there exist low-velocity or weak zones in the mid-lower crust, which are not evenly distributed beneath the SE margin of Tibetan plateau.

A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

CISK-rossby wave and the 30-60 Day Oscillation in the Tropics

The 30-60 day oscillation is an important aspect of the atmospheric variance in the tropical area. A number of works have been done on this phenomenon, this article is a further one. A quasi-geostrophic linear model that consists of a two-layer free atmosphere and a well-mixed boundary layer is used to investigate the instability of intraseasonal oscillation, its propagation and vertical structures. Results show that the dynamical coupling and interaction between the barotropic and baroclinic components via boundary layer convergence / divergence are responsible for the appearance of a new kind of low-frequency wave. Such wave is very different from the traditional tropical Rossby wave. It can propagate westward and eastward. Some behaviours of it appear to resemble the observed 30-60 day oscillation mode in many aspects, such,as vertical structures, zonal and meridional propagations. Now many researchers emphasize the direct relationship between CISK-Kelvin mode and the tropical atmospheric 30-60 oscillation. It is considered that CISK-Rossby mode should not be neglected.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Nonlinear Three-Wave Interaction among Barotropic Rossby Waves in a Large-scale Forced Barotropic Flow

In this paper. the coupling equations describing nonlinear three-wave interaction amongRossby waves including the forcing of an external vorticity source are obtained. Under certainconditions, the coupling equations with a constant amplitude forcing, the stability analysis indicates that when the amplitude of the external forcing increases to a certain extent, a pitchforkbifurcation occurs. Also. it is shown fi-o m numerical results that the bifurcation can lead to chaoticbehavior of' strange' attractor. For the obtained three-variable equation, when the amplitude ofmodulated external forcing gradually increases, a Period-doubling bifurcation is found to lead tochaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forcedbarotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explainin part 30-60-day low-flequency oscillations observed in mid-high latitudes.

STUDY ON DYNAMICS OF TROPICAL CISK-ROSSBY WAVES AND MECHANISM OF 30-50 DAY OSCILLATIONS

To add to the growing mature research on the tropical 30-50 day oscillations from a new prospective, the current work bases on dynamic analysis of baroclinic quasi-geostrophic models to discuss dynamic mechanisms for the generation and propagation of CISK-Rossby waves, and to understand restraints and effects of different wave structures and thermodynamic forcing on the 30-50 day oscillations in the tropical atmosphere. Some important properties of the oscillation propagation have been explained and, in detail, with respect to its meridional propagation and vertical "baroclinic" structure. The work has come up with some new opinions and viewpoints. New opinions about the propagation and energy dispersion are to be proved by more observations and study.

Exact Traveling Wave Solutions of Nano-Ionic Solitons and Nano-Ionic Current of MTs Using the exp(-φ (ξ ))-Expansion Method

In this work, the exp(-φ (ξ )) -expansion method is used for the first time to investigate the exact traveling wave solutions involving parameters of nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. The validity and reliability of the method are tested by its applications to Nano-ionic solitons wave’s propagation along microtubules in living cells and Nano-ionic currents of MTs which play an important role in biology.

Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications

We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics.

Wavelet Analysis of Average

The identification method in the CurveExpert-1.40 software environment revealed asymmetric wavelets of changes in the average monthly temperature of New Delhi from 1931 to 2021.The maximum increment for 80 years of the average monthly temperature of 5.1℃was in March 2010.An analysis of the wave patterns of the dynamics of the average monthly temperature up to 2110 was carried out.For forecasting,formulas were adopted containing four components,among which the second component is the critical heat wave of India.The first component is the Mandelbrot law(in physics).It shows the natural trend of decreasing temperature.The second component increases according to the critical law.The third component with a correlation coefficient of 0.9522 has an annual fluctuation cycle.The fourth component with a semi-annual cycle shows the influence of vegetation cover.The warming level of 2010 will repeat again in 2035-2040.From 2040 the temperature will rise steadily.June is the hottest month.At the same time,the maximum temperature of 35.1℃in 2010 in June will again reach by 2076.But according to the second component of the heat wave,the temperature will rise from 0.54℃to 16.29°C.The annual and semi-annual cycles had an insignificant effect on the June temperature dynamics.Thus,the identification method on the example of meteorological observations in New Delhi made it possible to obtain summary models containing a different number of components.The temperature at a height of 2 m is insufficient.On the surface,according to space measurements,the temperature reaches 55°C.As a result,in order to identify more accurate asymmetric wavelets for forecasting,the results of satellite measurements of the surface temperature of India at various geographical locations of meteorological stations are additionally required.

Hypersonic boundary-layer transition on a flared cone

Transition on a flared cone with zero angle of at- tack was studied in our newly established Mach 6 quiet wind tunnel （M6QT） via wall pressure measurement and flow visualization. High-frequency pressure transducers were used to measure the second-mode waves＇ amplitudes and frequencies. Using pulsed schlieren diagnostic and Rayleigh scattering technique, we got a clear evolution of the second-mode disturbances. The second-mode waves exist for a long distance, which means that the second-mode waves grow linearly in a large region. Strong Mach waves are radiated from the edge of the boundary layer. With further development, the second-mode waves reach their maximum magnitude and harmonics of the second-mode instability appear. Then the disturbances grow nonlinearly. The second modes become weak and merge with each other. Finally, the nonlinear interaction of disturbance leads to a relatively quiet zone, which further breaks down, resulting in the transition of the bound- ary layer. Our results show that transition is determined by the second mode. The quiet zone before the final breakdown is observed in flow visualization for the first time. Eventual transition requires the presence of a quiet zone generated by nonlinear interactions.

The role of surface waves in the ocean mixed layer

Previously, most ocean circulation models have overlooked the role of the surface waves. As a result, these models have produced insufficient vertical mixing, with an under - prediction of the ,nixing layer （ML） depth and an over - prediction of the sea surface temperature （SST）, particularly during the summer season. As the ocean surface layer determines the lower boundary conditions of the atmosphere, this deficiency has severely limited the performance of the coupled ocean - atmospheric models and hence the climate studies. To overcome this shortcoming, a new parameterization for the wave effects in the ML model that will correct this systematic error of insufficient mixing. The new scheme has enabled the mixing layer to deepen, the surface excessive heating to be corrected, and an excellent agreement with observed global climatologic data. The study indicates that the surface waves are essential for ML formation, and that they are the primer drivers of the upper ocean dynamics; therefore, they are critical for climate studies.

Numerical simulation of characteristics of semidiurnal tidal waves in sea region around Taiwan

POM97, an oceanic model, has been used for the first time to the numerical study on the tidal waves of the as Regions around Taiwan. In this paper, we have got the result that the semidiurnal tidal waves of these area mainly are the co-operating tides which come from the south of 23'N of the western Pacific. Those semidiurnal tidal waves affecting the Taiwan Straits come respectively from the south and the north entrance of the channel, and the north tidal wave is stronger than the south one. The strongest tidal field is the area from the Meizhou Bay to the Xinhua Bay along the coast of Fujian Province, where the biggest amplitude of the M2 partial tide can reach 240 cm. The strongest tidal cur- rent fields lie in the Penghu watercourse, where the maximum velocity of the M2 partial tide can arrive at 196 m/s. In the horizontal structure of the tidal currets, we have found that there is a stream dot in the north of the channel, besides, there still exist four new ones. As for the vertical structure, it mainly is biassed to the right at the surface, and to the left near the bottom layer.

A New Pursuit Mode of Nonlinear Wave Surface

The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.

Gamma-Ray Bursts: Afterglows and Central Engines

Gamma-ray bursts (GRBs) are the most intense transient gamma-ray events in the sky; this, together with the strong evidence (the isotropic and inhomogeneous distribution of GRBs detected by BASTE) that they are located at cosmological distances, makes them the most energetic events ever known. For example, the observed radiation energies of some GRBs are equivalent to the total convertion into radiation of the mass energy of more than one solar mass. This is thousand times stronger than the energy of a supernova explosion. Some unconventional energy mechanism and extremely high conversion efficiency for these mysterious events are required. The discovery of host galaxies and association with supernovae at cosmological distances by the recently launched satellite of BeppoSAX and ground based radio and optical telescopes in GRB afterglow provides further support to the cosmological origin of GRBs and put strong constraints on their central engine. It is the aim of this article to review the possible central engines, energy mechanisms, dynamical and spectral evolution of GRBs, especially focusing on the afterglows in multi-wavebands.

Proton and He^(2+) Temperature Anisotropies in the Solar Wind Driven by Ion Cyclotron Waves

We carried out one-dimensional hybrid simulations of resonant scattering of protons and He2+ ions by ion cyclotron waves in an initially homogeneous, collisionless and magnetized plasma. The initial ion cyclotron waves have a power spectrum and propagate both outward and inward. Due to the resonant interaction with the protons and He2+ ions, the wave power will be depleted in the resonance region. Both the protons and He2+ ions can be resonantly heated in the direction perpendicular to the ambient magnetic field and leading to anisotropic velocity distributions, with the anisotropy higher for the He2+ ions than for the protons. At the same time, the anisotropies of the protons and He2+ ions are inversely correlated with the plasma β||p= 8πnpkBT||p/b02, consistent with the prediction of the quasilinear theory (QLT).