Painlevé Property and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

A class of coupled nonlinear Schrdinger equations:Painlev'e property,exact solutions,and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation

A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method.

Painlev property of the modified C-KdV equation and its exact solutions

In this paper, the Painleve properties of the modified C-KdV equation are verified by using the W-K algorithm. Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software, respectively.

Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation

The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.

若干非线性偏微分方程的Painleve性质和Backlund变换

若干非线性偏微分方程的Ｐａｉｎｌｅｖé性质和Ｂａｃｋｌｕｎｄ变换朱佐农（扬州大学农学院，扬州２２５００１）对于一个非线性偏微分方程，判别其可积性是重要的课题．Ｊ．Ｗｅｉｓｓ等人对偏微分方程定义了Ｐａｉｎｌｅｖｅ性质，从Ｐａｉｎｌｅｖｅ性质的分析出发可...

两个新的Painlevé可积方程

Painlevé分析是测试给定系统可积性的一个有效工具.现给出两个新的非线性偏微分方程,并利用Kruskal简化方法证明了这两个方程都具有Painlevé性质.

耦合Burgers方程的Painlevé分析和相关性质

为研究耦合Burgers方程的可积性,利用WTC测试方法,给出了第一类Burgers方程的Painlevé性质和第二类Burgers方程的条件Painlevé性质,进而得到了第一类方程的变量分离解和第二类方程的(N2+3N+6/2)-参数Lie点对称群.

一类微分方程的约化及其约化方程的Painlevé分析

对一类非线性偏微分方程组进行行波约化和相似约化,使原来的偏微分方程约化为常微分方程,并对此常微分方程进行Painleve分析,进一步给出此类非线性偏微分方程约化后的常微分方程组只有“弱”Painleve性质,还给出微分方程具有“弱”Painleve性质的一个例证。

广义kdv方程,广义mkdv方程的Painlevé分析

本文讨论了广义kdv、广义mkdv方程的Painleve性质。由此得到了广义kdv方程的Lax对和自Backlund变换;同时也得到了广义mkdv方程的自Backlund变换;最后讨论了与之相关的Schwarzian导数。

耿方程的Painlevé性质、Bcklund变换及其精确解

利用Painlevé分析的WTC方法,验证了耿方程具有Painlevé性质并给出其自Bcklund变换.通过Painlevé截断展开法,给出双曲函数型与三角函数型的孤立波解、定态解和有理解.

变系数Zakharov－Kuznetsov方程的容许变换和Painlev分析

讨论了来自于磁化的等离子体中非线性离子声波传播的Ｚａｋｈａｒｏｖ－Ｋｕｚｎｅｔｓｏｖ（ＺＫ）方程及变系数ＺＫ方程。得到了ＺＫ方程的奇性流形方程的通解；证明了变系数ＺＫ方程能够通过容许变换化为ＺＫ方程的系数所应满足的条件并不等价于它具条件ｐａｉｎｌｅｖ性质时的系数所应满足的条件。

A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.

Microstructure and tensile properties of AM50A magnesium alloy prepared by recrystallisation and partial melting process

Prior to thixoextrusion, the microstructural evolution of semi-solid AM50A magnesium alloy prepared by the recrystallisation and partial remelting (RAP) route was investigated.The effect of compressive ratio on microstructure of semi-solid AM50A magnesium alloy was studied.Furthermore, tensile properties of thixoextruded components were determined.The results showed that the occurrence of recrystallised grains was closely associated with the location of the first liquid formed above the solidus.With prolonging holding time, deformed microstructure was penetrated, causing fragmentation, which resulted in the decrease of average grain size.Moreover, prolonging holding time was favorable for the improvement of the degree of spheroidization due to the increase in the amount of liquid.With the increase in compressive ratio, the size of solid grain decreased, the degree of spheroidization was improved during partial remelting, and the tensile properties of thixoextruded AM50A components were improved.The tensile properties for AM50A magnesium alloy thixoextruded from starting material produced by the RAP route were better than those of the same alloy produced by die-casting and thixomolding.

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

Stable structure and optical properties of fused silica with NBOHC-E' defect

First-principles method is used to simulate the stable structure and optical properties of a 96-atom fused silica.The preferable structure of NBOHC-E＇（non-bridging oxygen hole center（NBOHC） and E＇ center） pair defect is predicted to be located at 2.4 A^° for the Si-O bond length.The quasi-particle GOWO calculations are performed and an accurate band gap is obtained in order to calculate the optical absorption properties.With the stretching of the Sil-O1 bond,an obvious redshift can be observed in the absorption spectrum.In the case of NBOHC-E＇ pair,the p-orbital DOS of Si1 atom will shift to the conduction band.Two obvious absorption peaks can be observed in the absorption spectrum.The calculation reproduced the peak positions of the well-known optical absorption bands.

Electro-optical properties and(E,F) phase diagram of fluorinated chiral smectic liquid crystals

Fluorinated smectic liquid crystals each with a biphenyl benzoate rigid core are investigated. Molecular structures of the studied compounds have difference only in fluorine position and the length of the carbon chain. Dielectric relaxation study and electro-optical measurements are carried out with the classical SSFLC geometry. The field-induced phase transitions are studied and the（E,T） phase diagram is established.

Effect of Fillers on Mechanical Properties and Fracture Toughness of Glass Fabric Reinforced Epoxy Composites

Plain weave woven glass fabric reinforced epoxy (G-E) composite filled with two different types of fillers namely graphite, silicon carbide (each 5 and 10 wt%) was fabricated by hand lay-up method and compressed using hot press. These composites were investigated for their static mechanical properties such as tensile, flexural properties and impact strength as well as mode-I fracture toughness as per ASTM standards. Experimental results on mechanical properties indicate that the strength and the modulus in tensile and flexural mode for G-E composite increase with increasing filler loading. The unfilled G-E composite has the tensile strength of 305 MPa and increased to 404.2 MPa for 10 wt% silicon carbide. However, in three-point bend mode, addition of graphite in G-E showed the highest flexural strength as well as modulus. Mode-I fracture toughness test results indicated that the graphite filler loading improved the toughness of G-E composite. Selected failed samples under tensile, bending and mode-I fracture were examined using scanning electron microscope to identify the fracture features.

一类变系数 KP 方程的 Painleve 分析和容许变换

讨论一类来自于表面波传播的变系数ＫＰ方程的完全可积性．证明了此类方程通过容许变换化为常系数ＫＰ方程或Ｋｄｖ方程时系数所应满足的条件，此条件即为此类方程完全可积的充分必要条件．

Effects of heavy metal on dielectric properties of E. coli revealed by dielectric spectroscopy

Dielectric spectroscopy of E. coli cell before and after exposure to heavy metals Cd^2＋ , Cu^2＋ , Zn^2＋ and Ca^2＋ was investigated. The results indicate that changes in dielectric spectra reflect effects of heavy metal on the structure and function of E. coli cells. Heavy metal can change membrane capacitance as well as pennittivity and conductivity of the cytoplasm. Changes in volume fraction suggested that dielectric measurement could monitor the growth of E. coli cells. These results demonstrated that dielectric spectroscopy was a potential effective technique for studying electric properties of biological cells.