Lie Symmetry Groups of （2＋1）-Dimensional BKP Equation and Its New Solutions

A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional B KP equation we get its symmetry. Furthermore, the exact solutions of （2＋1）-dimensional BKP equation are obtained through symmetry analysis.     

Similarity Reductions of Nearly Concentric KdV Equation

Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.     

Block （or Hamiltonian） Lie Symmetry of Dispersionless D-Type Drinfeld-Sokolov Hierarchy

In this paper, the dispersionless D-type Drinfeld-Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.     

Similarity Reductions of （2＋1）-Dimensional Multi-component Broer-Kaup System

Painleve property of the （2＋1）-dimensional multi-component Broer-Kaup （BK） system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal （CK） direct method to the （2＋1）- dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the （2＋1）-dimensional multi-component BK system.     

Symmetry and Exact Solutions of （2＋1）-Dimensional Generalized Sasa-Satsuma Equation via a Modified Direct Method

In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groups, of the well-known （2＋1）-dimensional Generalized Sasa-Satsuma （GSS） equation. Second, based on a modified direct method proposed by Lou [J.Phys.A： Math. Gen. 38 （2005） L129], more general symmetry groups are obtained and the relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groups obtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equations are constructed by the relationship obtained in the paper between the new solution and known solution.     

New Exact Solutions and Evolution of Solitons in Background Waves for （2＋1）-Dimensional Modified Dispersive Water-Wave System

With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.     

Approximate symmetry reduction for perturbed nonlinear SchrSdinger equation

We investigate the one-dimensional nonlinear SchrSdinger equation with a perturbation of polynomial type. The approximate symmetries and approximate symmetry reduction equations are obtained with the approximate symmetry perturbation theory.     

Solitons for the cubic-quintic nonlinear Schr顜僤inger 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.     

Symmetry Analysis and Similarity Solutions of a Resonant Davey-Stewartson System

Lie point symmetry analysis is performed to a recently proposed （2＋1）-dimensional nonlinear system, the resonant Davey-Stewartson equation. Some similarity solutions of the RDS equation are thus obtained.     

Similarity Reductions and Exact Solutions of a Coupled Korteweg de Vries System

For a special coupled Korteweg de Vries （KdV） system, its similarity solutions and reduction equations are obtained by the Clarkson and Kruskal＇s direct method. In addition, its new explicit soliton solutions and traveling wave solutions are found by the deformation and mapping method.     

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 （1999） 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 （2007） 056318] are retrieved.     

Similarity Reductions of Nonisospectral KP Equation by a Direct Method

On bases of the direct method developed by Clarkson and Kruskal [J. Math. Phys. 27 （1989） 2201], the （2＋1）-dimensional nonisospectral Kadomtsev-Petviashvili （KP） equation has been reduced to three types of （1 ＋1）- dimensional partial differential equations. We focus on solving the third type of reduction and dividing them into three subcases, from which we obtain rich solutions including some arbitrary functions.     

Symmetry Analysis of Nonlinear Incompressible Non-Hydrostatic Boussinesq Equations

The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.     

Symmetry, Reductions and New Exact Solutions of ANNV Equation Through Lax Pair

In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.     

Have we found conclusive evidence for dark matter through direct detection experiments？

A WIMP-model-independent method is used to examine the existing evidence for low mass dark matter. Using XENON100＇s recent result of 224.6 live days × 34 kg exposure and PICASSO＇s result that was published in 2012, we have obtained constraints on the couplings │an│ 〈 0.4 and │ap│ 〈 0.3, corresponding to spin-dependent cross-sections of σ〈2.5×10^-38 cm2 and σp〈1.4×10^-38cm2 for a WIMP mass of 10 GeV/c2. It is shown that the spin-independent isospin-violating dark matter model also fails to reconcile the recent result from XENON100 with the positive results from DAMA, CoGeNT and CDMS-Ⅱ.     

Invariance of Painlev6 property for some reduced （1 ＋ 1）-dimensional equations

We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.     

Application of wavelet-based active magnet power supply filter in accelerator

Since modern accelerators demand excellent stability to magnet power supply （PS）, it is necessary to decrease harmonic currents passing magnets. Aiming at depressing the rappel current from the PS in the Beijing electron-positron collider Ⅱ, a wavelet-based active power filter （APF） is proposed in this paper. An APF is an effective device to improve the quality of currents. As a countermeasure to these harmonic currents, the APF circuit generates a harmonic current, countervailing harmonic current from PS. An active power filter based on wavelet transformation is proposed. Discrete wavelet transformation is used to analyze the harmonic components in the supply current, and an active power filter circuit works according to the analysis results. Our simulation and experiment results are given to prove the effect of the APF.     

Symmetry Reduction and Exact Solutions of the （3＋1）-Dimensional Breaking Soliton Equation

By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the （3＋1）-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the （3＋1）-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the （3＋1）-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the （3＋ 1）-dimensional breaking soliton equation.     

Quantum Communication Scheme Using Non-symmetric Quantum Channel

A theoretical quantum communication scheme based on entanglement swapping and superdense coding is proposed with a 3-dimensional Bell state and 2-dimensional Bell state function as quantum channel, quantum key distribution and quantum secure direct communication can be simultaneously accomplished in the scheme. The scheme is secure and has high source capacity. At last, we generalize the quantum communication scheme to d-dimensional quantum channel     

Implementation of the direct demodulation method for natural gamma ray spectral logging

Spectrum analysis of natural gamma ray spectral logging （SGR） data is a critical part of surface informa- tion processing systems. Due to the low resolution, which is an inherent weakness of SGR, and the low signal-to-noise ratio problem of logging measurements, SGR is usually treated with a low confidence level. The Direct Demodulation （DD） method is an advanced technique to solve modulation equations interactively under physical constraints. It has higher sensitivity and spatial resolution than the traditional methods and can effectively suppress the logging noise. Based on standard count rate spectral data obtained from the China Offshore Oil Logging Company SGR Calibration Facility, this paper presents the application of the DD method to gamma-ray logging. The results are compared with four traditional algorithmic methods, showing that the DD method is a credible choice, with higher sensitivity and higher spatial resolution in gamma-ray log interpretation. The Point-Spread-Function of the Shengli Oil Logging Company＇s natural gamma ray spectroscopy instrument is obtained for the first time. The quantities of various radionuclides in their calibration pits are also obtained. The DD method was applied successfully to gamma-ray logging, offering a new option for SGR logging algorithm selection.