复合函数-微分方程亚纯解的性质

该文致力于研究两个问题.首先,考虑了如下一类复合函数-微分方程(w')^nw^(n)=aw^n+1(g)+bw+d亚纯解的存在性问题,得到了当a≠0,b,d是复常数且w是一个超越亚纯函数时,则g必为线性的.其次,鉴于方程和方程组之间的本质区别,研究复合函数方程组是有意义的.该文也考虑了一类复合函数方程组,在适当限制条件下,得到了其亚纯解的存在形式.有例子表明文中的结论是成立的.

Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations

The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition.

Solutions to a Class of Differential-fuctional Equations

In this paper, we study the solutions to a class of equations such as f(2z)=2f(z)f (z).Some related problems are discussed.

Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation

The bilinear form for a nonisospectral and variable-coefficient KdV equation is obtained and some exact soliton solutions are derived through Hirota method and Wronskian technique. We also derive the bilmear transformation from its Lax pairs and End solutions with the help of the obtained bilinear transformation.

Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid

The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method(HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter(ε) whereas it decreases by increasing the fluid material parameter(δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.

Applications of Extended Mapping Deformation Method in Two （3＋1）-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.

Exact Solutions to a Combined sinh-cosh-Gordon Equation

Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation

Approximate Analytical Solutions for Scattering States of D-dimensional Hulthen Potentials

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.

Multi-linear Variable Separation Approach to Solve a (2+1)-DimensionalGeneralization of Nonlinear Schroedinger System

By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.

On Stability of Solutions of a Certain Fourth-Order Functional Differential Equations

Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well known results.

Analysis of free vibration characteristic of steel-concrete composite box-girder considering shear lag and slip

Based on Hamilton principle,the governing differential equations and the corresponding boundary conditions of steel-concrete composite box girder with consideration of the shear lag effect meeting self equilibrated stress,shear deformation,slip,as well as rotational inertia were induced.Therefore,natural frequency equations were obtained for the boundary types,such as simple support,cantilever,continuous girder and fixed support at two ends.The ANSYS finite element solutions were compared with the analytical solutions by calculation examples and the validity of the proposed approach was verified,which also shows the correctness of longitudinal warping displacement functions.Some meaningful conclusions for engineering design were obtained.The decrease extent of each order natural frequency of the steel-concrete composite box-girder is great under action of the shear lag effect.The shear-lag effect of steel-concrete composite box girder increases when frequency order rises,and increases while span-width ratio decreases.The proposed approach provides theoretical basis for further research of free vibration characteristics of steel-concrete composite box-girder.

Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to （1＋1）-Dimensional Dispersive Long Wave Equation

In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.

New Predictor-Corrector Methods Based on Exponential Time Differencing forSystems of Nonlinear Differential Equations

We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.

Explicit Solutions of (2+1)-Dimensional Canonical Generalized KP, KdV, and (2+1)-Dimensional Burgers Equations with Variable Coefficients

In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burgers equations with variable coetticients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.

Exact Solutions of (2+1)-Dimensional Boiti-Leon-Pempinelle Equation with (G'/G)-Expansion Method

In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization

When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation.

Stability and Boundedness of Retarded Liénard-type Equation

This paper aims to investigate the retarded Liénard-type equation+f 1(x)+f 2(x)(t-τ)+f 3(x)2+φ(x)+g(x(t-τ))=0,where τ is a nonnegative constant, f 1,f 2,f 3,φ and g are continuous functions on R. Using Liapunov functional method, we establish a sufficient condition on the stability and boundedness of the solutions of above equation. This will generalize the main results of reference [2].

Some Notes of p-Moment Boundedness of Nonlinear Differential Equation with Pandom Impulses

A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.

Some Remarks on Exp-Function Method and Its Applications

Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.