New Exact Solutions and Conservation Laws to （3＋1）-Dimensional Potential-YTSF Equation

Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.

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.

Symmetry Groups and New Exact Solutions to （2＋1）-Dimensional Variable Coefficient Canonical Generalized KP Equation

In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.

Diversity of New Three-Wave Solutions and New Periodic Waves for the (3 + 1)-Dimensional Kadomtsev-Petviashvili-Boussinesq-Like Equation

Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These new solutions, named three-wave solutions and periodic wave have greatly enriched the existing literature. Via the three-dimensional images, density images and contour plots, the physical characteristics of these waves are well described. The new three-wave solutions and periodic solitary wave solutions obtained in this paper, will have a wide range of applications in the fields of physics and mechanics.

New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.

New Exact Solutions for a Class of Nonlinear Coupled Differential Equations

More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.

The New Infinite Sequence Solutions of Multiple Sine-Gordon Equations

By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, and the new solutions are obtained. First, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is changed to the problem of solving the solutions of the nonlinear ordinary differential equation. Second, with the help of the B?cklund transformation and the nonlinear superposition formula of solutions of the first kind of elliptic equation and the Riccati equation, the new infinite sequence soliton-like solutions of two kinds of sine-Gordon equations are constructed.

Some Kinds of New Composite Solutions of a Kind of Coupled Schrodinger Equation

With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schr?dinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the B?cklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schr?dinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.

GERBER TECHNOLOGY LAUNCHES FIRST OF NEW SERIES OF CUTTING SOLUTIONS

Precision, Productivity and Performance def ine the GERBERcutter? Z7Tolland, Conn., USA – Gerber Technology, a business unit of Gerber Scientific, Inc. (NYSE: GRB), and the world leader in providing innovative integrated software and hardware automation systems to

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

New Generalized Transformation Method and Its Application in Higher-Dimensional Soliton Equation

A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.

A New Solution in Understanding Massive White Dwarfs

The observed high over-luminous type-Ia supernovae imply the existence of super-Chandrasekhar limit white dwarfs, which raises a challenge to the classical white dwarf theories. By employing the Eddington-inspired Born-Infeld （EiBI） gravity, we reinvestigate the structures and properties of white dwarfs, and find out that the EiBI gravity provides a new way to understand the observations. It is shown that by choosing an appropriate positive Eddington parameter k, a massive white dwarf with mass up to 2.8M can be supported by the equation of state of free electron gas. Unlike the classical white dwarf theory, the maximum mass of the white dwarf sequence in the EiBI gravity is not decided by the mass radius relations, but is decided by the central density, pc = 4.3 × 1014 kg/ms, above which neutronization cannot be avoided and the white dwarf will transform into a neutron star. On the other hand, if the gravity in the massive white dwarf really behaves as the EiBI gravity predicts, then one can obtain a constraint on the Eddington parameter in the EiBI gravity, that is, 87rpokG/c2 ≥ 80 （where po =- 10^18 kg/m3） to support a massive white dwarf with mass up to 2.8M. Moreover, we find out that the fast Keplarian frequency of the massive white dwarf raises a degeneration between the two kinds of compact stars, that is, one cannot distinguish whether the observed massive pulsar is a massive neutron star or a massive white dwarf only through the observed pulse frequency and mass.

ZTE Launches New Generation Convergence Solution

ZTE Corporation,a leading global provider of telecommunications equipment and network solutions,launched its new-generation IMS-based solution (ZIMS),at the Global NGN Summit 2007 held in Beijing,China.

FULL SATISFACTION WITH FULL SERVICE ACCESS. TALK TO US ABOUT OUR NEW ZTE GPON SOLUTION.

With ZTE new GPON solution you’ll get new opportunities for increased bandwidth services to your customers.

FULL SATISFACTION WITH FULL SERVICE ACCESS.TALK TO US ABOUT OUR NEW ZTE GPON SOLUTION

With ZTE new GPON solution you’ll get new opportunities for increased bandwidth services to your customers.

ZTE Softswitch the Working Solution to Build the New Generation Network

ZTE Softswitch supports the interoperability and convergence oflegacy PSTN/ISDN, PLMN, IN, and the Internet, allowing operatorsor service providers to offer diversified services to any subscriber atany time on a ZTE Softswitch network.With powerful C4 and C5 features, ZTE Softswitch effectivelysolves the evolution problems in the existing networks, protectinglegacy network investment and reducing future investment to a prof-itable level for providers.

ZTE Debuts New Generation IPTN Bearer Network Solution

ZTE Corporation announced the formal launch of its new generation IPTN bearer network solution targeting mobile backhaul and multi-service delivery to meet the needs of IP-based services on August 27,2009.It features packet

ZTE Cloud Radio Solution to Usher in New Era of High-Performance LTE Networks

ZTE showcased its innovative cloud radio solution for 4G network optimization at the Mobile Asia Expo in Shanghai.

A Chinese Solution Multiparty cooperation and political consultation provide a new way to view democracy

On March 4, President Xi Jinping, also General Secretary of the Communist Party of China （CPC） Central Committee, attended a joint panel discussion with political advisors from the China Democratic League and the China Zhi Gong Party, those without party affiliation and those from the sector of returned over seas Chinese.

New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrdinger Equations

The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.