New Families of Rational Form Variable Separation Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.     

(3+1)维Burgers系统的瞬内嵌孤子和瞬锥形孤子

利用投射方程法和变量分离法,得到了(3+1)维Burgers系统的变量分离解(包括孤波解、周期波解和有理函数解).根据孤波解和有理函数解,构造出Burgers系统新颖的局域结构,例如瞬内嵌孤子和瞬锥形孤子.     

扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用

利用改进的 Riccati方程映射法和变量分离法, 得到了扩展的(2+1)维浅水波方程的变量分离解(包括孤波解, 周期波解和有理函数解). 根据得到的孤波解, 构造出了方程的几种不同形状的尖峰孤子结构, 研究了孤子的相互作用.     

Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave－short-wave resonant interaction

A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave－short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.     

Complex Wave Excitations in Generalized Broer-Kaup System

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.     

Fusion and fission solitons for the (2+1)-dimensional generalized Breor-Kaup system

With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional generalized Breor-Kaup (GBK) system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons.     

Annihilation Solitons and Chaotic Solitons for the （2＋1）-Dimensional Breaking Soliton System

By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.     

Variable separation solutions and new solitary wave structures to the （l＋l）-dimensional Ito system

A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1+1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.     

Localized Excitations of (2+1)-Dimensional Korteweg-de Vries System Derived from a Periodic Wave Solution

With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2 1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.     

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Using the projective Riccati equation expansion (PREE) method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.     

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.

(Some figures in this article are in colour only in the electronic version)     

Neutrino wave function and oscillation suppression

We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the electron is relativistic and the spatial size of its wave packet is much larger than the size of the crystal cell, then the wave packet of the produced neutrino has essentially the same size as the wave packet of the electron. We investigate the suppression of neutrino oscillations at large distances caused by two mechanisms: (1) spatial separation of wave packets corresponding to different neutrino masses; (2) neutrino energy dispersion for given neutrino mass eigenstates. We resolve the contributions of these two mechanisms. Received: 26 July 2005, Published online: 6 October 2005     

Imaging and control of interfering wave packets in a dissociating molecule

Using two identical 110 femtosecond (fs) optical pulses separated by 310 fs, we launch two dissociative wave packets in I2. We measure the square of the wave function as a function of both the internuclear separation, /Psi(R)/(2), and of the internuclear velocity, /Psi(v(R))/(2), by ionizing the dissociating molecule with an intense 20 fs probe pulse. Strong interference is observed in both /Psi(R)/(2) and in /Psi(v(R))/(2). The interference, and therefore the shape of the wave function, is controlled through the phase difference between the two dissociation pulses in good agreement with calculations.     

Complex wave excitations general （2＋1）-dimensional and chaotic patterns for a Korteweg-de Vries system

Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV     

Doubly Periodic Propagating Wave for （2d-1）-Dimensional Breaking Soliton Equation

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.     

Difference between a photon's momentum and an atom's recoil

When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.     

Quantum-phase resolved mapping of ground-state vibrational D2 wave packets via selective depletion in intense laser pulses

Applying 7 fs pump-probe pulses (780 nm, 4 x 10(14) W/cm2) we observe electronic ground-state vibrational wave packets in neutral D2 with a period of T=11.101(70) fs by following the internuclear separation (R-)dependent ionization with a sensitivity of Delta相似文献   

Variable Separation Solutions in (1+1)-Dimensional and (3+1)-Dimensional Systems via Entangled Mapping Approach

In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1 1)-dimensional and (3 1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1 1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3 1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.     

GNSS clock corrections densification at SHAO: from 5 min to 30 s

High frequency multi-GNSS zero-difference applications like Precise Orbit Determination(POD)for Low Earth Orbiters(LEO)and high frequency kinematic positioning require corresponding high-rate GNSS clock corrections.The determination of the GNSS clocks in the orbit determination process is time consuming,especially in the combined GPS/GLONASS processing.At present,a large number of IGS Analysis Centers(AC)provide clock corrections in 5-min sampling and only a few ACs provide clocks in 30-s sampling for both GPS and GLONASS.In this paper,an efficient epoch-difference GNSS clock determination algorithm is adopted based on the algorithm used by the Center for Orbit Determination in Europe(CODE).The clock determination procedure of the GNSS Analysis Center at Shanghai Astronomical Observatory(SHAO)and the algorithm is described in detail.It is shown that the approach greatly speeds up the processing,and the densified 30-s clocks have the same quality as the 5-min clocks estimated based on a zero-difference solution.Comparing the densified 30-s GNSS clocks provided by SHAO with that of IGS and its ACs,results show that our 30-s GNSS clocks are of the same quality as that of IGS.Allan deviation also gives the same conclusion.Further validation of the SHAO 30-s clock product is performed in kinematic PPP and LEO POD.Results indicate that the positions have the same accuracy when using SHAO 30-s GNSS clocks or IGS(and its AC)finals.The robustness of the algorithm and processing approach ensure its extension to provide clocks in 5-s or even higher frequencies.The implementation of the new approach is simple and it could be delivered as a black-box to the current scientific software packages.